Edit Profile (opens in new tab) Robinson, James Cooper Compute Distance To: Compute Author ID: robinson.james-c Published as: Robinson, James C.; Robinson, J. C. Homepage: https://warwick.ac.uk/fac/sci/maths/people/staff/james_robinson/ External Links: MGP · ORCID · dblp Documents Indexed: 136 Publications since 1993, including 6 Books 6 Contributions as Editor · 1 Further Contribution Co-Authors: 53 Co-Authors with 108 Joint Publications 1,449 Co-Co-Authors all top 5 Co-Authors 34 single-authored 27 Langa, Jose’ Antonio 13 Rodrigo, José Luis 13 Sadowski, Witold 10 Nolasco de Carvalho, Alexandre 9 Suárez, Antonio 9 Vidal-López, Alejandro 8 Olson, Eric J. 7 Caraballo Garrido, Tomás 6 McCormick, David S. 6 Rodríguez-Bernal, Aníbal 6 Sierżȩga, Mikołaj 5 Dashti, Masoumeh 5 Friz, Peter Karl 4 Laister, Robert 4 Marín-Rubio, Pedro 4 Pinto de Moura, Eleonora 3 Fefferman, Charles Louis 3 Sharples, Nicholas 2 Fraser, Jonathan MacDonald 2 Glendinning, Paul Alexander 2 Hajduk, Karol W. 2 Hoang, Luan Thach 2 Kukavica, Igor 2 Łukaszewicz, Grzegorz 2 Margaris, Alexandros 2 Pooley, Benjamin C. 2 Real Anguas, José 2 Sánchez-Gabites, Jaime J. 2 Skipper, Jack W. D. 1 Blömker, Dirk 1 Bosia, Stefano 1 Chemin, Jean-Yves 1 Chernyshenko, Sergei I. 1 Chipot, Michel 1 Constantin, Peter 1 Cotter, Simon L. 1 Crauel, Hans 1 Cunha, Arthur C. 1 Da Silva, Ricardo Parreira 1 Droniou, Jérôme 1 Galdi, Giovanni Paolo 1 García-Luengo, Julia 1 Henderson, A. M. 1 Hieber, Matthias 1 Nieuwenhuis, Michaela A. C. 1 Nolde, Christian 1 Ożański, Wojciech Sławomir 1 Pata, Vittorino 1 Planas, Gabriela 1 Shibata, Yoshihiro 1 Steinerberger, Stefan 1 Stuart, Andrew M. 1 Tearne, Oliver M. 1 Titi, Edriss Saleh 1 Xue, Wei 1 Zhou, Yi all top 5 Serials 16 Journal of Differential Equations 14 Nonlinearity 9 Journal of Mathematical Analysis and Applications 7 Discrete and Continuous Dynamical Systems 5 Proceedings of the American Mathematical Society 4 Physica D 4 Journal of Dynamics and Differential Equations 4 London Mathematical Society Lecture Note Series 3 Archive for Rational Mechanics and Analysis 3 Physics Letters. A 3 Advances in Mathematics 3 Real Analysis Exchange 3 SIAM Journal on Mathematical Analysis 3 Proceedings of the Royal Society of London. Series A. Mathematical, Physical and Engineering Sciences 3 Discrete and Continuous Dynamical Systems. Series B 3 Stochastics and Dynamics 2 Communications in Mathematical Physics 2 Journal of Mathematical Physics 2 Asymptotic Analysis 2 Dynamic Systems and Applications 2 Journal of Mathematical Fluid Mechanics 2 Comptes Rendus. Mathématique. Académie des Sciences, Paris 1 Inverse Problems 1 Journal of Fluid Mechanics 1 Mathematical Proceedings of the Cambridge Philosophical Society 1 Bulletin of the London Mathematical Society 1 Journal of Functional Analysis 1 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 1 Rendiconti del Seminario Matematico della Università di Padova 1 SIAM Journal on Numerical Analysis 1 Transactions of the American Mathematical Society 1 Ergodic Theory and Dynamical Systems 1 Systems & Control Letters 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 Numerical Algorithms 1 Communications in Partial Differential Equations 1 Journal de Mathématiques Pures et Appliquées. Neuvième Série 1 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 1 Set-Valued Analysis 1 Chaos 1 Revista Matemática Complutense 1 Communications on Pure and Applied Analysis 1 Milan Journal of Mathematics 1 Analysis and Applications (Singapore) 1 Mediterranean Journal of Mathematics 1 Dynamics of Partial Differential Equations 1 Applied Mathematical Sciences 1 Cambridge Studies in Advanced Mathematics 1 Cambridge Tracts in Mathematics 1 Lecture Notes in Mathematics 1 NATO Science Series II: Mathematics, Physics and Chemistry 1 ISRN Mathematical Analysis 1 Boletín de la Sociedad Española de Matemática Aplicada. S\(\vec{\text{e}}\)MA 1 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences 1 Cambridge Texts in Applied Mathematics all top 5 Fields 91 Partial differential equations (35-XX) 59 Dynamical systems and ergodic theory (37-XX) 46 Fluid mechanics (76-XX) 31 Ordinary differential equations (34-XX) 12 General topology (54-XX) 10 Functional analysis (46-XX) 10 Probability theory and stochastic processes (60-XX) 9 Measure and integration (28-XX) 9 Operator theory (47-XX) 8 Numerical analysis (65-XX) 7 General and overarching topics; collections (00-XX) 5 Manifolds and cell complexes (57-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Classical thermodynamics, heat transfer (80-XX) 1 Algebraic geometry (14-XX) 1 Functions of a complex variable (30-XX) 1 Difference and functional equations (39-XX) 1 Convex and discrete geometry (52-XX) 1 Differential geometry (53-XX) 1 Statistics (62-XX) 1 Mechanics of deformable solids (74-XX) 1 Biology and other natural sciences (92-XX) 1 Systems theory; control (93-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 122 Publications have been cited 2,566 times in 1,680 Documents Cited by ▼ Year ▼ Infinite-dimensional dynamical systems. An introduction to dissipative parabolic PDEs and the theory of global attractors. Zbl 0980.35001Robinson, James C. 363 2001 Attractors for infinite-dimensional non-autonomous dynamical systems. Zbl 1263.37002Carvalho, Alexandre N.; Langa, José A.; Robinson, James C. 240 2013 Introduction (to “From finite to infinite dimensional dynamical systems”). Zbl 1026.37500Robinson, J. C.; Glendinning, P. A. 205 2001 Higher order commutator estimates and local existence for the non-resistive MHD equations and related models. Zbl 1296.35142Fefferman, Charles L.; McCormick, David S.; Robinson, James C.; Rodrigo, Jose L. 97 2014 Upper semicontinuity of attractors for small random perturbations of dynamical systems. Zbl 0917.35169Caraballo, Tomás; Langa, José A.; Robinson, James C. 79 1998 The three-dimensional Navier-Stokes equations. Classical theory. Zbl 1358.35002Robinson, James C.; Rodrigo, José L.; Sadowski, Witold 76 2016 Dimensions, embeddings, and attractors. Zbl 1222.37004Robinson, James C. 57 2011 Local existence for the non-resistive MHD equations in Besov spaces. Zbl 1333.35183Chemin, Jean-Yves; McCormick, David S.; Robinson, James C.; Rodrigo, Jose L. 53 2016 Stability and random attractors for a reaction-diffusion equation with multiplicative noise. Zbl 1011.37031Caraballo, Tomás; Langa, José A.; Robinson, James C. 52 2000 A comparison between two theories for multi-valued semiflows and their asymptotic behaviour. Zbl 1053.47050Caraballo, T.; Marín-Rubio, P.; Robinson, J. C. 52 2003 A stochastic pitchfork bifurcation in a reaction-diffusion equation. Zbl 0996.60070Caraballo, Tomás; Langa, José A.; Robinson, James C. 49 2001 Characterization of non-autonomous attractors of a perturbed infinite-dimensional gradient system. Zbl 1119.37023Carvalho, Alexandre N.; Langa, José A.; Robinson, James C.; Suárez, Antonio 44 2007 Stability, instability, and bifurcation phenomena in non-autonomous differential equations. Zbl 1004.37032Langa, José A.; Robinson, James C.; Suárez, Antonio 43 2002 Local existence for the non-resistive MHD equations in nearly optimal Sobolev spaces. Zbl 1359.35150Fefferman, Charles L.; McCormick, David S.; Robinson, James C.; Rodrigo, Jose L. 42 2017 Structure and bifurcation of pullback attractors in a non-autonomous Chafee-Infante equation. Zbl 1282.35042Carvalho, A. N.; Langa, J. A.; Robinson, J. C. 40 2012 Stability of random attractors under perturbation and approximation. Zbl 1020.37033Robinson, James C. 40 2002 Invariant measures for dissipative systems and generalised Banach limits. Zbl 1230.37094Łukaszewicz, Grzegorz; Real, José; Robinson, James C. 32 2011 Attractors for differential equations with variable delays. Zbl 0997.34073Caraballo, Tomás; Langa, José A.; Robinson, James C. 31 2001 Generalised Gagliardo-Nirenberg inequalities using weak Lebesgue spaces and BMO. Zbl 1291.46029McCormick, David S.; Robinson, James C.; Rodrigo, Jose L. 30 2013 Bayesian inverse problems for functions and applications to fluid mechanics. Zbl 1228.35269Cotter, S. L.; Dashti, M.; Robinson, J. C.; Stuart, A. M. 30 2009 Invariant measures for non-autonomous dissipative dynamical systems. Zbl 1351.37076Łukaszewicz, Grzegorz; Robinson, James C. 29 2014 On the Assouad dimension of self-similar sets with overlaps. Zbl 1317.28014Fraser, J. M.; Henderson, A. M.; Olson, E. J.; Robinson, J. C. 27 2015 Global attractors: Topology and finite-dimensional dynamics. Zbl 0953.34049Robinson, James C. 26 1999 Fractal dimension of a random invariant set. Zbl 1134.37364Langa, José A.; Robinson, James C. 26 2006 Supersolutions for a class of semilinear heat equations. Zbl 1334.35169Robinson, James C.; Sierżęga, Mikołaj 26 2013 The effect of noise on the Chafee-Infante equation: a nonlinear case study. Zbl 1173.60022Caraballo, Tomás; Crauel, Hans; Langa, José A.; Robinson, James C. 25 2007 Energy equality for the 3D critical convective Brinkman-Forchheimer equations. Zbl 1379.35242Hajduk, Karol W.; Robinson, James C. 25 2017 On the continuity of pullback attractors for evolution processes. Zbl 1175.37078Carvalho, Alexandre N.; Langa, José A.; Robinson, James C. 23 2009 A posteriori regularity of the three-dimensional Navier-Stokes equations from numerical computations. Zbl 1144.81329Chernyshenko, Sergei I.; Constantin, Peter; Robinson, James C.; Titi, Edriss S. 23 2007 Lower bounds on blow up solutions of the three-dimensional Navier-Stokes equations in homogeneous Sobolev spaces. Zbl 1425.76055Robinson, James C.; Sadowski, Witold; Silva, Ricardo P. 22 2012 The stability of attractors for non-autonomous perturbations of gradient-like systems. Zbl 1115.37064Langa, José A.; Robinson, James C.; Suárez, Antonio; Vidal-López, Alejandro 20 2007 A topological delay embedding theorem for infinite-dimensional dynamical systems. Zbl 1084.37063Robinson, James C. 19 2005 A weak-\(L^p\) Prodi-Serrin type regularity criterion for the Navier-Stokes equations. Zbl 1307.35186Bosia, Stefano; Pata, Vittorino; Robinson, James C. 19 2014 Bifurcations in non-autonomous scalar equations. Zbl 1096.34026Langa, J. A.; Robinson, J. C.; Suárez, A. 18 2006 On the continuity of global attractors. Zbl 1356.37027Hoang, Luan T.; Olson, Eric J.; Robinson, James C. 18 2015 Almost-everywhere uniqueness of Lagrangian trajectories for suitable weak solutions of the three-dimensional Navier-Stokes equations. Zbl 1173.35631Robinson, James C.; Sadowski, Witold 18 2009 Lower semicontinuity of attractors for non-autonomous dynamical systems. Zbl 1181.37016Carvalho, Alexandre N.; Langa, José A.; Robinson, James C. 18 2009 A complete characterisation of local existence for semilinear heat equations in Lebesgue spaces. Zbl 1349.35169Laister, R.; Robinson, J. C.; Sierżȩga, M.; Vidal-López, A. 17 2016 Pullback attractors and extremal complete trajectories for non-autonomous reaction-diffusion problems. Zbl 1137.35009Robinson, James C.; Rodríguez-Bernal, Aníbal; Vidal-López, Alejandro 17 2007 Non-autonomous dynamical systems. Zbl 1384.37024Carvalho, Alexandre N.; Langa, José A.; Robinson, James C. 17 2015 Stabilisation of linear PDEs by Stratonovich noise. Zbl 1157.60332Caraballo, Tomás; Robinson, James C. 16 2004 Continuity of pullback and uniform attractors. Zbl 1383.37011Hoang, Luan T.; Olson, Eric J.; Robinson, James C. 16 2018 Attractors for the stochastic 3D Navier-Stokes equations. Zbl 1059.35100Marín-Rubio, Pedro; Robinson, James C. 15 2003 The asymptotic completeness of inertial manifolds. Zbl 0898.35016Robinson, James C. 15 1996 Decay of weak solutions and the singular set of the three-dimensional Navier-Stokes equations. Zbl 1120.35075Robinson, James C.; Sadowski, Witold 14 2007 Attractors and finite-dimensional behaviour in the 2D Navier-Stokes equations. Zbl 1286.35198Robinson, James C. 14 2013 Almost bi-Lipschitz embeddings and almost homogeneous sets. Zbl 1197.54045Olson, Eric J.; Robinson, James C. 13 2010 On the dimension of the singular set of solutions to the Navier-Stokes equations. Zbl 1233.35162Robinson, James C.; Sadowski, Witold 12 2012 Rigorous numerical verification of uniqueness and smoothness in a surface growth model. Zbl 1315.65092Blömker, Dirk; Nolde, Christian; Robinson, James C. 12 2015 Forwards and pullback behaviour of a non-autonomous Lotka-Volterra system. Zbl 1044.34009Langa, José A.; Robinson, James C.; Suárez, Antonio 12 2003 Existence and nonexistence of unbounded forwards attractor for a class of non-autonomous reaction diffusion equations. Zbl 1126.37008Langa, J. A.; Robinson, J. C.; Rodríguez-Bernal, A.; Suárez, A.; Vidal-López, A. 11 2007 Existence and uniqueness for a coupled parabolic-elliptic model with applications to magnetic relaxation. Zbl 1317.35206McCormick, David S.; Robinson, James C.; Rodrigo, Jose L. 11 2014 Linear embeddings of finite-dimensional subsets of Banach spaces into Euclidean spaces. Zbl 1163.54008Robinson, James C. 11 2009 Inertial manifolds for the Kuramoto-Sivashinsky equation. Zbl 0941.35511Robinson, James C. 10 1994 Partial regularity for a surface growth model. Zbl 1408.35065Ożański, Wojciech S.; Robinson, James C. 10 2019 Permanence and asymptotically stable complete trajectories for nonautonomous Lotka-Volterra models with diffusion. Zbl 1185.35119Langa, José A.; Robinson, James C.; Rodríguez-Bernal, Aníbal; Suárez, Antonio 10 2009 An introduction to ordinary differential equations. Zbl 1053.34001Robinson, James C. 10 2004 Smooth attractors have zero “thickness”. Zbl 0971.37011Friz, Peter K.; Robinson, James C. 9 1999 A local smoothness criterion for solutions of the 3D Navier-Stokes equations. Zbl 1296.35123Robinson, James C.; Sadowski, Witold 9 2014 The motion of a fluid–rigid disc system at the zero limit of the rigid disc radius. Zbl 1294.76082Dashti, Masoumeh; Robinson, James C. 9 2011 Parametrising the attractor of the two-dimensional Navier-Stokes equations with a finite number of nodal values. Zbl 1076.35090Friz, P. K.; Robinson, J. C. 9 2001 An a posteriori condition on the numerical approximations of the Navier-Stokes equations for the existence of a strong solution. Zbl 1235.76022Dashti, Masoumeh; Robinson, James C. 9 2008 Solutions of the 3D Navier-Stokes equations for initial data in \(\dot H^{1/2}\): robustness of regularity and numerical verification of regularity for bounded sets of initial data in. Zbl 1310.35190Marín-Rubio, Pedro; Robinson, James C.; Sadowski, Witold 8 2013 Pullback attractors for the non-autonomous 2D Navier-Stokes equations for minimally regular forcing. Zbl 1277.35064García-Luengo, Julia; Marín-Rubio, Pedro; Real, José; Robinson, James C. 8 2014 Generalised Cantor sets and the dimension of products. Zbl 1371.28024Olson, Eric J.; Robinson, James C.; Sharples, Nicholas 8 2016 Numerical verification of regularity in the three-dimensional Navier-Stokes equations for bounded sets of initial data. Zbl 1155.35071Robinson, James C.; Sadowski, Witold 8 2008 Nodal parametrisation of analytic attractors. Zbl 1153.37439Friz, Peter K.; Kukavica, Igor; Robinson, James C. 8 2001 Well-posedness for the diffusive 3D Burgers equations with initial data in \(H^{1/2}\). Zbl 1365.35079Pooley, Benjamin C.; Robinson, James C. 7 2016 Non-existence of local solutions for semilinear heat equations of Osgood type. Zbl 1319.35108Laister, R.; Robinson, J. C.; Sierżȩga, M. 7 2013 A concise proof of the ”geometric” construction of inertial manifolds. Zbl 1020.34509Robinson, James C. 6 1995 Distinguishing smooth functions by a finite number of point values, and a version of the Takens embedding theorem. Zbl 1058.35045Kukavica, Igor; Robinson, James C. 6 2004 Computing inertial manifolds. Zbl 1032.34060Robinson, James C. 6 2002 Strict inequality in the box-counting dimension product formulas. Zbl 1277.28014Robinson, James C.; Sharples, Nicholas 6 2013 Embedding of global attractors and their dynamics. Zbl 1250.37032Pinto de Moura, Eleonora; Robinson, James C.; Sánchez-Gabites, J. J. 6 2011 A rigorous treatment of ‘experimental’ observations for the two-dimensional Navier-Stokes equations. Zbl 1013.35062Robinson, James C. 6 2001 A criterion for uniqueness of Lagrangian trajectories for weak solutions of the 3D Navier-Stokes equations. Zbl 1186.35146Robinson, James C.; Sadowski, Witold 6 2009 Lipschitz deviation and embeddings of global attractors. Zbl 1213.37112Pinto de Moura, Eleonora; Robinson, James C. 6 2010 Determining asymptotic behavior from the dynamics on attracting sets. Zbl 0933.34059Langa, José A.; Robinson, James C. 5 1999 A note on well-posedness of semilinear reaction-diffusion problem with singular initial data. Zbl 1227.35095Robinson, James C.; Sierżȩga, Mikołaj 5 2012 Inertial manifolds and the cone condition. Zbl 0787.34036Robinson, James C. 5 1993 Pullback permanence in a non-autonomous competitive Lotka–Volterra model. Zbl 1027.35017Langa, J. A.; Robinson, J. C.; Suárez, A. 5 2003 Inertial manifolds with and without delay. Zbl 0954.37037Robinson, James C. 5 1999 A finite number of point observations which determine a non-autonomous fluid flow. Zbl 1193.37103Langa, José A.; Robinson, James C. 5 2001 A coupled particle-continuum model: Well-posedness and the limit of zero radius. Zbl 1063.76106Robinson, James C. 4 2004 Robustness of regularity for the 3D convective Brinkman-Forchheimer equations. Zbl 1476.35196Hajduk, Karol W.; Robinson, James C.; Sadowski, Witold 4 2021 Energy conservation for the Euler equations on \(\mathbb{T}^2 \times \mathbb{R}_+\) for weak solutions defined without reference to the pressure. Zbl 1417.35104Robinson, James C.; Rodrigo, José L.; Skipper, Jack W. D. 4 2018 A simple proof of uniqueness of the particle trajectories for solutions of the Navier-Stokes equations. Zbl 1165.35424Dashti, M.; Robinson, J. C. 4 2009 Orthogonal sequences and regularity of embeddings into finite-dimensional spaces. Zbl 1206.46023Pinto de Moura, E.; Robinson, J. C. 4 2010 Minimal periods of semilinear evolution equations with Lipschitz nonlinearity. Zbl 1087.34037Robinson, James C.; Vidal-López, Alejandro 3 2006 Arbitrarily accurate approximate inertial manifolds of fixed dimension. Zbl 1052.34509Robinson, James C. 3 1997 Regularity and singularity in the three-dimensional Navier-Stokes equations. Zbl 1244.35106Robinson, James C. 3 2006 Dimension prints and the avoidance of sets for flow solutions of non-autonomous ordinary differential equations. Zbl 1321.34020Robinson, James C.; Sharples, Nicholas 3 2013 Bifurcation from zero of a complete trajectory for nonautonomous logistic PDEs. Zbl 1092.35514Langa, José A.; Robinson, James C.; Suárez, Antonio 3 2005 Some closure results for inertial manifolds. Zbl 0901.34053Robinson, J. C. 3 1997 A necessary and sufficient condition for uniqueness of the trivial solution in semilinear parabolic equations. Zbl 1372.35156Laister, R.; Robinson, J. C.; Sierżęga, M. 3 2017 Non-existence of local solutions of semilinear heat equations of Osgood type in bounded domains. (Non-existence de solutions locales pour les équations de la chaleur semi-linéaires de type Osgood dans des domaines bornés.) Zbl 1297.35114Laister, Robert; Robinson, James C.; Sierżȩga, Mikolaj 3 2014 A topological time-delay embeddding theorem for infinite-dimensional cocycle dynamical systems. Zbl 1149.37011Robinson, J. C. 3 2008 Finite-dimensional global attractors in Banach spaces. Zbl 1215.35038Carvalho, Alexandre N.; Langa, José A.; Robinson, James C. 3 2010 Low dimensional attractors arise from forcing at small scales. Zbl 1040.35063Robinson, James C. 3 2003 Finite-dimensional behavior in dissipative partial differential equations. Zbl 1055.35501Robinson, J. C. 3 1995 Robustness of regularity for the 3D convective Brinkman-Forchheimer equations. Zbl 1476.35196Hajduk, Karol W.; Robinson, James C.; Sadowski, Witold 4 2021 Mathematical analysis of the Navier-Stokes equations. Lecture notes given at the CIME school on mathematical analysis of the Navier-Stokes equations: foundations and overview of basic open problems, Cetraro, Italy, September 4–8, 2017. Zbl 1443.35002 2 2020 The Navier-Stokes regularity problem. Zbl 1462.35251Robinson, James C. 1 2020 Partial regularity for the 3D Navier-Stokes equations. Zbl 1442.35309Robinson, James C. 1 2020 Partial regularity for a surface growth model. Zbl 1408.35065Ożański, Wojciech S.; Robinson, James C. 10 2019 Embedding properties of sets with finite box-counting dimension. Zbl 1428.37020Margaris, Alexandros; Robinson, James C. 2 2019 Continuity of pullback and uniform attractors. Zbl 1383.37011Hoang, Luan T.; Olson, Eric J.; Robinson, James C. 16 2018 Energy conservation for the Euler equations on \(\mathbb{T}^2 \times \mathbb{R}_+\) for weak solutions defined without reference to the pressure. Zbl 1417.35104Robinson, James C.; Rodrigo, José L.; Skipper, Jack W. D. 4 2018 Optimal existence classes and nonlinear-like dynamics in the linear heat equation in \(\mathbb{R}^d\). Zbl 1400.35151Robinson, James C.; Rodríguez-Bernal, Aníbal 2 2018 Energy conservation in the 3D Euler equations on \({\mathbb T}^2 \times {\mathbb R}_+\). Zbl 1408.35139Robinson, James C.; Rodrigo, José L.; Skipper, Jack W. D. 1 2018 Local existence for the non-resistive MHD equations in nearly optimal Sobolev spaces. Zbl 1359.35150Fefferman, Charles L.; McCormick, David S.; Robinson, James C.; Rodrigo, Jose L. 42 2017 Energy equality for the 3D critical convective Brinkman-Forchheimer equations. Zbl 1379.35242Hajduk, Karol W.; Robinson, James C. 25 2017 A necessary and sufficient condition for uniqueness of the trivial solution in semilinear parabolic equations. Zbl 1372.35156Laister, R.; Robinson, J. C.; Sierżęga, M. 3 2017 The three-dimensional Navier-Stokes equations. Classical theory. Zbl 1358.35002Robinson, James C.; Rodrigo, José L.; Sadowski, Witold 76 2016 Local existence for the non-resistive MHD equations in Besov spaces. Zbl 1333.35183Chemin, Jean-Yves; McCormick, David S.; Robinson, James C.; Rodrigo, Jose L. 53 2016 A complete characterisation of local existence for semilinear heat equations in Lebesgue spaces. Zbl 1349.35169Laister, R.; Robinson, J. C.; Sierżȩga, M.; Vidal-López, A. 17 2016 Generalised Cantor sets and the dimension of products. Zbl 1371.28024Olson, Eric J.; Robinson, James C.; Sharples, Nicholas 8 2016 Well-posedness for the diffusive 3D Burgers equations with initial data in \(H^{1/2}\). Zbl 1365.35079Pooley, Benjamin C.; Robinson, James C. 7 2016 On finite-dimensional global attractors of homeomorphisms. Zbl 1362.37066Robinson, James C.; Sánchez-Gabites, Jaime J. 2 2016 Lower bounds on blowing-up solutions of the three-dimensional Navier-Stokes equations in \(\dot H^{3/2}\), \(\dot H^{5/2}\), and \(\dot B^{5/2}_{2,1}\). Zbl 1344.35081McCormick, David S.; Olson, Eric J.; Robinson, James C.; Rodrigo, Jose L.; Vidal-López, Alejandro; Zhou, Yi 2 2016 An Eulerian-Lagrangian form for the Euler equations in Sobolev spaces. Zbl 1359.76041Pooley, Benjamin C.; Robinson, James C. 1 2016 On the Assouad dimension of self-similar sets with overlaps. Zbl 1317.28014Fraser, J. M.; Henderson, A. M.; Olson, E. J.; Robinson, J. C. 27 2015 On the continuity of global attractors. Zbl 1356.37027Hoang, Luan T.; Olson, Eric J.; Robinson, James C. 18 2015 Non-autonomous dynamical systems. Zbl 1384.37024Carvalho, Alexandre N.; Langa, José A.; Robinson, James C. 17 2015 Rigorous numerical verification of uniqueness and smoothness in a surface growth model. Zbl 1315.65092Blömker, Dirk; Nolde, Christian; Robinson, James C. 12 2015 A simple example concerning the upper box-counting dimension of a Cartesian product. Zbl 1384.28008Olson, Eric J.; Robinson, James C. 1 2015 Higher order commutator estimates and local existence for the non-resistive MHD equations and related models. Zbl 1296.35142Fefferman, Charles L.; McCormick, David S.; Robinson, James C.; Rodrigo, Jose L. 97 2014 Invariant measures for non-autonomous dissipative dynamical systems. Zbl 1351.37076Łukaszewicz, Grzegorz; Robinson, James C. 29 2014 A weak-\(L^p\) Prodi-Serrin type regularity criterion for the Navier-Stokes equations. Zbl 1307.35186Bosia, Stefano; Pata, Vittorino; Robinson, James C. 19 2014 Existence and uniqueness for a coupled parabolic-elliptic model with applications to magnetic relaxation. Zbl 1317.35206McCormick, David S.; Robinson, James C.; Rodrigo, Jose L. 11 2014 A local smoothness criterion for solutions of the 3D Navier-Stokes equations. Zbl 1296.35123Robinson, James C.; Sadowski, Witold 9 2014 Pullback attractors for the non-autonomous 2D Navier-Stokes equations for minimally regular forcing. Zbl 1277.35064García-Luengo, Julia; Marín-Rubio, Pedro; Real, José; Robinson, James C. 8 2014 Non-existence of local solutions of semilinear heat equations of Osgood type in bounded domains. (Non-existence de solutions locales pour les équations de la chaleur semi-linéaires de type Osgood dans des domaines bornés.) Zbl 1297.35114Laister, Robert; Robinson, James C.; Sierżȩga, Mikolaj 3 2014 Log-Lipschitz embeddings of homogeneous sets with sharp logarithmic exponents and slicing products of balls. Zbl 1314.46029Robinson, James C. 2 2014 Log-Lipschitz continuity of the vector field on the attractor of certain parabolic equations. Zbl 1315.35038De Moura, Eleonora Pinto; Robinson, James C. 2 2014 Minimal periods for ordinary differential equations in strictly convex Banach spaces and explicit bounds for some \(L^p\)-spaces. Zbl 1287.34032Nieuwenhuis, Michaela A. C.; Robinson, James C.; Steinerberger, Stefan 1 2014 Attractors for infinite-dimensional non-autonomous dynamical systems. Zbl 1263.37002Carvalho, Alexandre N.; Langa, José A.; Robinson, James C. 240 2013 Generalised Gagliardo-Nirenberg inequalities using weak Lebesgue spaces and BMO. Zbl 1291.46029McCormick, David S.; Robinson, James C.; Rodrigo, Jose L. 30 2013 Supersolutions for a class of semilinear heat equations. Zbl 1334.35169Robinson, James C.; Sierżęga, Mikołaj 26 2013 Attractors and finite-dimensional behaviour in the 2D Navier-Stokes equations. Zbl 1286.35198Robinson, James C. 14 2013 Solutions of the 3D Navier-Stokes equations for initial data in \(\dot H^{1/2}\): robustness of regularity and numerical verification of regularity for bounded sets of initial data in. Zbl 1310.35190Marín-Rubio, Pedro; Robinson, James C.; Sadowski, Witold 8 2013 Non-existence of local solutions for semilinear heat equations of Osgood type. Zbl 1319.35108Laister, R.; Robinson, J. C.; Sierżȩga, M. 7 2013 Strict inequality in the box-counting dimension product formulas. Zbl 1277.28014Robinson, James C.; Sharples, Nicholas 6 2013 Dimension prints and the avoidance of sets for flow solutions of non-autonomous ordinary differential equations. Zbl 1321.34020Robinson, James C.; Sharples, Nicholas 3 2013 Minimal periods of semilinear evolution equations with Lipschitz nonlinearity revisited. Zbl 1284.34056Robinson, James C.; Vidal-López, Alejandro 2 2013 Structure and bifurcation of pullback attractors in a non-autonomous Chafee-Infante equation. Zbl 1282.35042Carvalho, A. N.; Langa, J. A.; Robinson, J. C. 40 2012 Lower bounds on blow up solutions of the three-dimensional Navier-Stokes equations in homogeneous Sobolev spaces. Zbl 1425.76055Robinson, James C.; Sadowski, Witold; Silva, Ricardo P. 22 2012 On the dimension of the singular set of solutions to the Navier-Stokes equations. Zbl 1233.35162Robinson, James C.; Sadowski, Witold 12 2012 A note on well-posedness of semilinear reaction-diffusion problem with singular initial data. Zbl 1227.35095Robinson, James C.; Sierżȩga, Mikołaj 5 2012 Dimensions, embeddings, and attractors. Zbl 1222.37004Robinson, James C. 57 2011 Invariant measures for dissipative systems and generalised Banach limits. Zbl 1230.37094Łukaszewicz, Grzegorz; Real, José; Robinson, James C. 32 2011 The motion of a fluid–rigid disc system at the zero limit of the rigid disc radius. Zbl 1294.76082Dashti, Masoumeh; Robinson, James C. 9 2011 Embedding of global attractors and their dynamics. Zbl 1250.37032Pinto de Moura, Eleonora; Robinson, James C.; Sánchez-Gabites, J. J. 6 2011 Almost bi-Lipschitz embeddings and almost homogeneous sets. Zbl 1197.54045Olson, Eric J.; Robinson, James C. 13 2010 Lipschitz deviation and embeddings of global attractors. Zbl 1213.37112Pinto de Moura, Eleonora; Robinson, James C. 6 2010 Orthogonal sequences and regularity of embeddings into finite-dimensional spaces. Zbl 1206.46023Pinto de Moura, E.; Robinson, J. C. 4 2010 Finite-dimensional global attractors in Banach spaces. Zbl 1215.35038Carvalho, Alexandre N.; Langa, José A.; Robinson, James C. 3 2010 Bayesian inverse problems for functions and applications to fluid mechanics. Zbl 1228.35269Cotter, S. L.; Dashti, M.; Robinson, J. C.; Stuart, A. M. 30 2009 On the continuity of pullback attractors for evolution processes. Zbl 1175.37078Carvalho, Alexandre N.; Langa, José A.; Robinson, James C. 23 2009 Almost-everywhere uniqueness of Lagrangian trajectories for suitable weak solutions of the three-dimensional Navier-Stokes equations. Zbl 1173.35631Robinson, James C.; Sadowski, Witold 18 2009 Lower semicontinuity of attractors for non-autonomous dynamical systems. Zbl 1181.37016Carvalho, Alexandre N.; Langa, José A.; Robinson, James C. 18 2009 Linear embeddings of finite-dimensional subsets of Banach spaces into Euclidean spaces. Zbl 1163.54008Robinson, James C. 11 2009 Permanence and asymptotically stable complete trajectories for nonautonomous Lotka-Volterra models with diffusion. Zbl 1185.35119Langa, José A.; Robinson, James C.; Rodríguez-Bernal, Aníbal; Suárez, Antonio 10 2009 A criterion for uniqueness of Lagrangian trajectories for weak solutions of the 3D Navier-Stokes equations. Zbl 1186.35146Robinson, James C.; Sadowski, Witold 6 2009 A simple proof of uniqueness of the particle trajectories for solutions of the Navier-Stokes equations. Zbl 1165.35424Dashti, M.; Robinson, J. C. 4 2009 The regularity problem for the three-dimensional Navier-Stokes equations. Zbl 1387.35465Robinson, James C.; Sadowski, Witold 2 2009 An a posteriori condition on the numerical approximations of the Navier-Stokes equations for the existence of a strong solution. Zbl 1235.76022Dashti, Masoumeh; Robinson, James C. 9 2008 Numerical verification of regularity in the three-dimensional Navier-Stokes equations for bounded sets of initial data. Zbl 1155.35071Robinson, James C.; Sadowski, Witold 8 2008 A topological time-delay embeddding theorem for infinite-dimensional cocycle dynamical systems. Zbl 1149.37011Robinson, J. C. 3 2008 Characterization of non-autonomous attractors of a perturbed infinite-dimensional gradient system. Zbl 1119.37023Carvalho, Alexandre N.; Langa, José A.; Robinson, James C.; Suárez, Antonio 44 2007 The effect of noise on the Chafee-Infante equation: a nonlinear case study. Zbl 1173.60022Caraballo, Tomás; Crauel, Hans; Langa, José A.; Robinson, James C. 25 2007 A posteriori regularity of the three-dimensional Navier-Stokes equations from numerical computations. Zbl 1144.81329Chernyshenko, Sergei I.; Constantin, Peter; Robinson, James C.; Titi, Edriss S. 23 2007 The stability of attractors for non-autonomous perturbations of gradient-like systems. Zbl 1115.37064Langa, José A.; Robinson, James C.; Suárez, Antonio; Vidal-López, Alejandro 20 2007 Pullback attractors and extremal complete trajectories for non-autonomous reaction-diffusion problems. Zbl 1137.35009Robinson, James C.; Rodríguez-Bernal, Aníbal; Vidal-López, Alejandro 17 2007 Decay of weak solutions and the singular set of the three-dimensional Navier-Stokes equations. Zbl 1120.35075Robinson, James C.; Sadowski, Witold 14 2007 Existence and nonexistence of unbounded forwards attractor for a class of non-autonomous reaction diffusion equations. Zbl 1126.37008Langa, J. A.; Robinson, J. C.; Rodríguez-Bernal, A.; Suárez, A.; Vidal-López, A. 11 2007 Parametrization of global attractors, experimental observations, and turbulence. Zbl 1175.76041Robinson, James C. 1 2007 Fractal dimension of a random invariant set. Zbl 1134.37364Langa, José A.; Robinson, James C. 26 2006 Bifurcations in non-autonomous scalar equations. Zbl 1096.34026Langa, J. A.; Robinson, J. C.; Suárez, A. 18 2006 Minimal periods of semilinear evolution equations with Lipschitz nonlinearity. Zbl 1087.34037Robinson, James C.; Vidal-López, Alejandro 3 2006 Regularity and singularity in the three-dimensional Navier-Stokes equations. Zbl 1244.35106Robinson, James C. 3 2006 A topological delay embedding theorem for infinite-dimensional dynamical systems. Zbl 1084.37063Robinson, James C. 19 2005 Bifurcation from zero of a complete trajectory for nonautonomous logistic PDEs. Zbl 1092.35514Langa, José A.; Robinson, James C.; Suárez, Antonio 3 2005 Stabilisation of linear PDEs by Stratonovich noise. Zbl 1157.60332Caraballo, Tomás; Robinson, James C. 16 2004 An introduction to ordinary differential equations. Zbl 1053.34001Robinson, James C. 10 2004 Distinguishing smooth functions by a finite number of point values, and a version of the Takens embedding theorem. Zbl 1058.35045Kukavica, Igor; Robinson, James C. 6 2004 A coupled particle-continuum model: Well-posedness and the limit of zero radius. Zbl 1063.76106Robinson, James C. 4 2004 Stability of random attractors for a backwards Euler scheme. Zbl 1082.37056Robinson, James C. 1 2004 A comparison between two theories for multi-valued semiflows and their asymptotic behaviour. Zbl 1053.47050Caraballo, T.; Marín-Rubio, P.; Robinson, J. C. 52 2003 Attractors for the stochastic 3D Navier-Stokes equations. Zbl 1059.35100Marín-Rubio, Pedro; Robinson, James C. 15 2003 Forwards and pullback behaviour of a non-autonomous Lotka-Volterra system. Zbl 1044.34009Langa, José A.; Robinson, James C.; Suárez, Antonio 12 2003 Pullback permanence in a non-autonomous competitive Lotka–Volterra model. Zbl 1027.35017Langa, J. A.; Robinson, J. C.; Suárez, A. 5 2003 Low dimensional attractors arise from forcing at small scales. Zbl 1040.35063Robinson, James C. 3 2003 Stability, instability, and bifurcation phenomena in non-autonomous differential equations. Zbl 1004.37032Langa, José A.; Robinson, James C.; Suárez, Antonio 43 2002 Stability of random attractors under perturbation and approximation. Zbl 1020.37033Robinson, James C. 40 2002 Computing inertial manifolds. Zbl 1032.34060Robinson, James C. 6 2002 Constructing an elementary measure on a space of projections. Zbl 1189.53072Friz, Peter K.; Robinson, James C. 1 2002 Infinite-dimensional dynamical systems. An introduction to dissipative parabolic PDEs and the theory of global attractors. Zbl 0980.35001Robinson, James C. 363 2001 Introduction (to “From finite to infinite dimensional dynamical systems”). Zbl 1026.37500Robinson, J. C.; Glendinning, P. A. 205 2001 A stochastic pitchfork bifurcation in a reaction-diffusion equation. Zbl 0996.60070Caraballo, Tomás; Langa, José A.; Robinson, James C. 49 2001 ...and 22 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 1,654 Authors 66 Robinson, James Cooper 56 Langa, Jose’ Antonio 55 Caraballo Garrido, Tomás 39 Kloeden, Peter Eris 38 Li, Yangrong 36 Nolasco de Carvalho, Alexandre 36 Zhong, Chengkui 32 Sun, Chunyou 32 Valero, José 29 Zhao, Caidi 25 Zhou, Shengfan 21 Cui, Hongyong 21 Marín-Rubio, Pedro 19 Freitas, Mirelson M. 19 Mohan, Manil Thankamani 17 Duan, Jinqiao 17 Fraser, Jonathan MacDonald 16 Cung The Anh 16 Li, Desheng 16 Titi, Edriss Saleh 15 Real Anguas, José 15 Yang, Meihua 15 Yang, Xinguang 14 Kapustyan, Oleksiy V. 14 Obaya, Rafael 14 Wang, Bixiang 14 Xie, Yongqin 14 Zelik, Sergey V. 13 Łukaszewicz, Grzegorz 13 Nascimento, Marcelo Jose Dias 13 You, Bo 12 Kukavica, Igor 12 Sanjurjo, José M. R. 12 Simsen, Jacson 12 Zhu, Kaixuan 11 Bezerra, Flank David Morais 11 Bortolan, Matheus Cheque 11 Olson, Eric J. 11 Stuart, Andrew M. 11 Wang, Renhai 11 Wang, Yejuan 11 You, Yuncheng 10 Kalita, Piotr 10 Ramos, Anderson J. A. 10 Wang, Jintao 10 Wu, Jiahong 10 Zhang, Qiangheng 10 Zhao, Wenqiang 10 Zhou, Feng 9 Barge Yáñez, Héctor 9 Bonotto, Everaldo M. 9 Czaja, Radosław 9 Larios, Adam 9 Li, Fang 9 Li, Fuzhi 9 Ożański, Wojciech Sławomir 9 Pizzocchero, Livio 9 Pötzsche, Christian 9 Schmalfuß, Björn 9 Yang, Lu 9 Yang, Zhijian 9 Yin, Jinyan 8 Blömker, Dirk 8 Cheskidov, Alexey 8 Foiaș, Ciprian 8 García-Luengo, Julia 8 Huang, Jianhua 8 Ishige, Kazuhiro 8 Li, Yanan 8 Liu, Hui 8 Meng, Fengjuan 8 Rasmussen, Martin 8 Rodrigo, José Luis 8 Tan, Wen 7 Anguiano, María 7 Chekroun, Mickaël D. 7 Colucci, Renato 7 Gess, Benjamin 7 Jiang, Zaihong 7 Kostianko, Anna 7 Li, Chunqiu 7 Li, Dandan 7 Lu, Kening 7 Ma, Qiaozhen 7 Ma, Shan 7 McCormick, David S. 7 Morosi, Carlo 7 Rodríguez-Bernal, Aníbal 7 Suárez, Antonio 7 Sun, Chengfeng 7 Wang, Yanqing 7 Yan, Xingjie 6 Alouini, Brahim 6 Cholewa, Jan W. 6 Guo, Boling 6 Han, Xiaoying 6 Jiang, Fei 6 Jolly, Michael Summerfield 6 Ju, Xuewei 6 Kasyanov, Pavlo O. ...and 1,554 more Authors all top 5 Cited in 297 Serials 154 Journal of Differential Equations 92 Journal of Mathematical Analysis and Applications 86 Nonlinear Analysis. 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New Series 3 Electronic Journal of Differential Equations (EJDE) 3 Advances in Differential Equations 3 Complexity 3 European Series in Applied and Industrial Mathematics (ESAIM): Control, Optimization and Calculus of Variations 3 Nonlinear Dynamics ...and 197 more Serials all top 5 Cited in 46 Fields 1,224 Partial differential equations (35-XX) 643 Dynamical systems and ergodic theory (37-XX) 476 Fluid mechanics (76-XX) 218 Probability theory and stochastic processes (60-XX) 170 Ordinary differential equations (34-XX) 98 Numerical analysis (65-XX) 72 Measure and integration (28-XX) 61 Systems theory; control (93-XX) 57 Biology and other natural sciences (92-XX) 56 Operator theory (47-XX) 48 Mechanics of deformable solids (74-XX) 37 Functional analysis (46-XX) 34 Geophysics (86-XX) 33 Real functions (26-XX) 26 Statistics (62-XX) 25 General topology (54-XX) 24 Statistical mechanics, structure of matter (82-XX) 21 Calculus of variations and optimal control; optimization (49-XX) 20 Harmonic analysis on Euclidean spaces (42-XX) 20 Global analysis, analysis on manifolds (58-XX) 18 Difference and functional equations (39-XX) 18 Classical thermodynamics, heat transfer (80-XX) 12 Integral equations (45-XX) 12 Mechanics of particles and systems (70-XX) 8 Manifolds and cell complexes (57-XX) 8 Computer science (68-XX) 7 Quantum theory (81-XX) 6 Differential geometry (53-XX) 6 Algebraic topology (55-XX) 6 Optics, electromagnetic theory (78-XX) 5 Operations research, mathematical programming (90-XX) 5 Information and communication theory, circuits (94-XX) 4 Linear and multilinear algebra; matrix theory (15-XX) 4 Functions of a complex variable (30-XX) 3 Number theory (11-XX) 2 Combinatorics (05-XX) 2 Algebraic geometry (14-XX) 2 Special functions (33-XX) 2 Approximations and expansions (41-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Mathematical logic and foundations (03-XX) 1 Topological groups, Lie groups (22-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Convex and discrete geometry (52-XX) 1 Astronomy and astrophysics (85-XX) 1 Mathematics education (97-XX) Citations by Year