Hittmeir, Sabine; Klein, Rupert; Li, Jinkai; Titi, Edriss S. Global well-posedness for the thermodynamically refined passively transported nonlinear moisture dynamics with phase changes. (English) Zbl 1528.35119 J. Nonlinear Sci. 33, No. 4, Paper No. 65, 24 p. (2023). Reviewer: Roberta Bianchini (Roma) MSC: 35Q35 35Q30 35Q86 35A01 35A02 35B45 35M86 35K10 76D03 76D09 86A10 PDFBibTeX XMLCite \textit{S. Hittmeir} et al., J. Nonlinear Sci. 33, No. 4, Paper No. 65, 24 p. (2023; Zbl 1528.35119) Full Text: DOI arXiv
Bardos, Claude W.; Nguyen, Trinh T.; Nguyen, Toan T.; Titi, Edriss S. The inviscid limit for the 2D Navier-Stokes equations in bounded domains. (English) Zbl 1497.35339 Kinet. Relat. Models 15, No. 3, 317-340 (2022). MSC: 35Q30 35Q35 76D05 76D10 PDFBibTeX XMLCite \textit{C. W. Bardos} et al., Kinet. Relat. Models 15, No. 3, 317--340 (2022; Zbl 1497.35339) Full Text: DOI arXiv
Lin, Quyuan; Liu, Xin; Titi, Edriss S. On the effect of fast rotation and vertical viscosity on the lifespan of the \(3D\) Primitive equations. (English) Zbl 1491.35342 J. Math. Fluid Mech. 24, No. 3, Paper No. 73, 44 p. (2022). MSC: 35Q35 35Q86 76D05 76E07 86A05 86A10 35A01 35A02 PDFBibTeX XMLCite \textit{Q. Lin} et al., J. Math. Fluid Mech. 24, No. 3, Paper No. 73, 44 p. (2022; Zbl 1491.35342) Full Text: DOI arXiv
Li, Jinkai; Titi, Edriss S.; Yuan, Guozhi The primitive equations approximation of the anisotropic horizontally viscous \(3D\) Navier-Stokes equations. (English) Zbl 1477.35126 J. Differ. Equations 306, 492-524 (2022). MSC: 35Q30 35Q86 76D05 86A05 86A10 PDFBibTeX XMLCite \textit{J. Li} et al., J. Differ. Equations 306, 492--524 (2022; Zbl 1477.35126) Full Text: DOI arXiv
Titi, Edriss S.; Trabelsi, Saber Global well-posedness of a three-dimensional Brinkman-Forchheimer-Bénard convection model in porous media. arXiv:2204.03531 Preprint, arXiv:2204.03531 [math.AP] (2022). MSC: 35Q30 35Q35 76B03 86A10 93C20 37C50 76B75 34D06 BibTeX Cite \textit{E. S. Titi} and \textit{S. Trabelsi}, ``Global well-posedness of a three-dimensional Brinkman-Forchheimer-B\'enard convection model in porous media'', Preprint, arXiv:2204.03531 [math.AP] (2022) Full Text: arXiv OA License
Hoang, Luan T.; Titi, Edriss S. Asymptotic expansions in time for rotating incompressible viscous fluids. (English) Zbl 1464.35182 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 38, No. 1, 109-137 (2021). MSC: 35Q30 76D05 35C20 76E07 35B05 35D30 76U05 PDFBibTeX XMLCite \textit{L. T. Hoang} and \textit{E. S. Titi}, Ann. Inst. Henri Poincaré, Anal. Non Linéaire 38, No. 1, 109--137 (2021; Zbl 1464.35182) Full Text: DOI arXiv
Ibdah, Hussain A.; Mondaini, Cecilia F.; Titi, Edriss S. Fully discrete numerical schemes of a data assimilation algorithm: uniform-in-time error estimates. (English) Zbl 1466.65154 IMA J. Numer. Anal. 40, No. 4, 2584-2625 (2020). MSC: 65M70 65M60 65M06 65M12 65M15 93B52 76D05 35Q30 PDFBibTeX XMLCite \textit{H. A. Ibdah} et al., IMA J. Numer. Anal. 40, No. 4, 2584--2625 (2020; Zbl 1466.65154) Full Text: DOI
Liu, Xin; Titi, Edriss S. Well-posedness of strong solutions to the anelastic equations of stratified viscous flows. (English) Zbl 1440.35240 J. Math. Fluid Mech. 22, No. 3, Paper No. 39, 25 p. (2020). MSC: 35Q30 35Q86 76D03 76D05 76D50 35D35 PDFBibTeX XMLCite \textit{X. Liu} and \textit{E. S. Titi}, J. Math. Fluid Mech. 22, No. 3, Paper No. 39, 25 p. (2020; Zbl 1440.35240) Full Text: DOI arXiv
Luo, Tianwen; Titi, Edriss S. Non-uniqueness of weak solutions to hyperviscous Navier-Stokes equations: on sharpness of J.-L. Lions exponent. (English) Zbl 1437.35542 Calc. Var. Partial Differ. Equ. 59, No. 3, Paper No. 92, 15 p. (2020). MSC: 35Q30 76D05 35D30 26A33 35R11 PDFBibTeX XMLCite \textit{T. Luo} and \textit{E. S. Titi}, Calc. Var. Partial Differ. Equ. 59, No. 3, Paper No. 92, 15 p. (2020; Zbl 1437.35542) Full Text: DOI arXiv
García-Archilla, Bosco; Novo, Julia; Titi, Edriss S. Uniform in time error estimates for a finite element method applied to a downscaling data assimilation algorithm for the Navier-Stokes equations. (English) Zbl 1448.65157 SIAM J. Numer. Anal. 58, No. 1, 410-429 (2020). Reviewer: Jürgen Socolowsky (Brandenburg an der Havel) MSC: 65M60 65M12 35Q30 65M15 65M20 76B75 65N30 65M70 PDFBibTeX XMLCite \textit{B. García-Archilla} et al., SIAM J. Numer. Anal. 58, No. 1, 410--429 (2020; Zbl 1448.65157) Full Text: DOI arXiv
Jiu, Quansen; Niu, Dongjuan; Titi, Edriss S.; Xin, Zhouping Axisymmetric \(3D\) Euler-\(\alpha\) equations without swirl: existence, uniqueness, and Radon measure valued solutions. (English) Zbl 1454.76033 Pure Appl. Funct. Anal. 4, No. 3, 573-588 (2019). MSC: 76B47 35Q30 PDFBibTeX XMLCite \textit{Q. Jiu} et al., Pure Appl. Funct. Anal. 4, No. 3, 573--588 (2019; Zbl 1454.76033) Full Text: arXiv Link
Titi, Edriss S.; Trabelsi, Saber Global well-posedness of a 3D MHD model in porous media. (English) Zbl 1431.76155 J. Geom. Mech. 11, No. 4, 621-637 (2019). MSC: 76W05 76S05 35Q30 35Q35 76B03 93C10 93C20 76B75 PDFBibTeX XMLCite \textit{E. S. Titi} and \textit{S. Trabelsi}, J. Geom. Mech. 11, No. 4, 621--637 (2019; Zbl 1431.76155) Full Text: DOI arXiv
Celik, Emine; Olson, Eric; Titi, Edriss S. Spectral filtering of interpolant observables for a discrete-in-time downscaling data assimilation algorithm. (English) Zbl 1428.35276 SIAM J. Appl. Dyn. Syst. 18, No. 2, 1118-1142 (2019). MSC: 35Q30 37C50 76B75 93C20 PDFBibTeX XMLCite \textit{E. Celik} et al., SIAM J. Appl. Dyn. Syst. 18, No. 2, 1118--1142 (2019; Zbl 1428.35276) Full Text: DOI arXiv
Farhat, Aseel; Lunasin, Evelyn; Titi, Edriss S. A data assimilation algorithm: the paradigm of the 3D Leray-\(\alpha\) model of turbulence. (English) Zbl 1436.35274 Ben Ayed, Mohamed (ed.) et al., Partial differential equations arising from physics and geometry. A volume in memory of Abbas Bahri. Based on the conference, Hammamet, Tunisia, March 20–29, 2015. Cambridge: Cambridge University Press. Lond. Math. Soc. Lect. Note Ser. 450, 253-273 (2019). MSC: 35Q30 93C20 37C50 76B75 34D06 76F02 76D05 35Q86 86A05 PDFBibTeX XMLCite \textit{A. Farhat} et al., Lond. Math. Soc. Lect. Note Ser. 450, 253--273 (2019; Zbl 1436.35274) Full Text: DOI arXiv Link
Bardos, Claude; Gwiazda, Piotr; Świerczewska-Gwiazda, Agnieszka; Titi, Edriss S.; Wiedemann, Emil On the extension of Onsager’s conjecture for general conservation laws. (English) Zbl 1420.35202 J. Nonlinear Sci. 29, No. 2, 501-510 (2019). MSC: 35Q31 35B33 76D05 PDFBibTeX XMLCite \textit{C. Bardos} et al., J. Nonlinear Sci. 29, No. 2, 501--510 (2019; Zbl 1420.35202) Full Text: DOI arXiv
Li, Jinkai; Titi, Edriss S. The primitive equations as the small aspect ratio limit of the Navier-Stokes equations: rigorous justification of the hydrostatic approximation. (English. French summary) Zbl 1412.35224 J. Math. Pures Appl. (9) 124, 30-58 (2019). MSC: 35Q30 35Q86 76D05 86A05 86A10 PDFBibTeX XMLCite \textit{J. Li} and \textit{E. S. Titi}, J. Math. Pures Appl. (9) 124, 30--58 (2019; Zbl 1412.35224) Full Text: DOI arXiv
Bardos, Claude; Titi, Edriss S. Onsager’s conjecture for the incompressible Euler equations in bounded domains. (English) Zbl 1390.35241 Arch. Ration. Mech. Anal. 228, No. 1, 197-207 (2018). MSC: 35Q31 76D05 PDFBibTeX XMLCite \textit{C. Bardos} and \textit{E. S. Titi}, Arch. Ration. Mech. Anal. 228, No. 1, 197--207 (2018; Zbl 1390.35241) Full Text: DOI arXiv
Mondaini, Cecilia F.; Titi, Edriss S. Uniform-in-time error estimates for the postprocessing Galerkin method applied to a data assimilation algorithm. (English) Zbl 1384.35067 SIAM J. Numer. Anal. 56, No. 1, 78-110 (2018). Reviewer: Piotr Biler (Wrocław) MSC: 35Q30 76B75 37L65 65M15 65M60 65M70 93C20 93B52 PDFBibTeX XMLCite \textit{C. F. Mondaini} and \textit{E. S. Titi}, SIAM J. Numer. Anal. 56, No. 1, 78--110 (2018; Zbl 1384.35067) Full Text: DOI
Ibdah, Hussain A.; Mondaini, Cecilia F.; Titi, Edriss S. Uniform in time error estimates for fully discrete numerical schemes of a data assimilation algorithm. arXiv:1805.01595 Preprint, arXiv:1805.01595 [math.NA] (2018). MSC: 35B42 35Q30 37L65 65M12 65M15 65M70 76B75 93B52 93C20 BibTeX Cite \textit{H. A. Ibdah} et al., ``Uniform in time error estimates for fully discrete numerical schemes of a data assimilation algorithm'', Preprint, arXiv:1805.01595 [math.NA] (2018) Full Text: arXiv OA License
Hittmeir, Sabine; Klein, Rupert; Li, Jinkai; Titi, Edriss S. Global well-posedness for passively transported nonlinear moisture dynamics with phase changes. (English) Zbl 1379.35325 Nonlinearity 30, No. 10, 3676-3718 (2017). Reviewer: Thomas Ernst (Uppsala) MSC: 35Q86 35A01 35B45 35D35 35M86 35Q30 35Q35 76D03 76D09 86A10 PDFBibTeX XMLCite \textit{S. Hittmeir} et al., Nonlinearity 30, No. 10, 3676--3718 (2017; Zbl 1379.35325) Full Text: DOI arXiv
Farhat, Aseel; Lunasin, Evelyn; Titi, Edriss S. Continuous data assimilation for a 2D Bénard convection system through horizontal velocity measurements alone. (English) Zbl 1365.35108 J. Nonlinear Sci. 27, No. 3, 1065-1087 (2017). MSC: 35Q30 93C20 37C50 76B75 34D06 PDFBibTeX XMLCite \textit{A. Farhat} et al., J. Nonlinear Sci. 27, No. 3, 1065--1087 (2017; Zbl 1365.35108) Full Text: DOI arXiv
Jolly, Michael S.; Martinez, Vincent R.; Titi, Edriss S. A data assimilation algorithm for the subcritical surface quasi-geostrophic equation. (English) Zbl 1358.35091 Adv. Nonlinear Stud. 17, No. 1, 167-192 (2017). MSC: 35Q30 37C50 76B75 34D06 35Q86 42B25 26A33 76B15 76U05 PDFBibTeX XMLCite \textit{M. S. Jolly} et al., Adv. Nonlinear Stud. 17, No. 1, 167--192 (2017; Zbl 1358.35091) Full Text: DOI arXiv
Li, Jinkai; Titi, Edriss S. Existence and uniqueness of weak solutions to viscous primitive equations for a certain class of discontinuous initial data. (English) Zbl 1364.35275 SIAM J. Math. Anal. 49, No. 1, 1-28 (2017). Reviewer: Jürgen Socolowsky (Brandenburg an der Havel) MSC: 35Q35 76D03 76D05 86A10 35D30 PDFBibTeX XMLCite \textit{J. Li} and \textit{E. S. Titi}, SIAM J. Math. Anal. 49, No. 1, 1--28 (2017; Zbl 1364.35275) Full Text: DOI arXiv
Gesho, Masakazu; Olson, Eric; Titi, Edriss S. A computational study of a data assimilation algorithm for the two-dimensional Navier-Stokes equations. (English) Zbl 1373.76027 Commun. Comput. Phys. 19, No. 4, 1094-1110 (2016). MSC: 76D05 35Q30 PDFBibTeX XMLCite \textit{M. Gesho} et al., Commun. Comput. Phys. 19, No. 4, 1094--1110 (2016; Zbl 1373.76027) Full Text: DOI arXiv
Foias, Ciprian; Mondaini, Cecilia F.; Titi, Edriss S. A discrete data assimilation scheme for the solutions of the two-dimensional Navier-Stokes equations and their statistics. (English) Zbl 1362.35208 SIAM J. Appl. Dyn. Syst. 15, No. 4, 2109-2142 (2016). Reviewer: Dmitry Pelinovsky (Hamilton) MSC: 35Q30 37C50 76B75 93C20 PDFBibTeX XMLCite \textit{C. Foias} et al., SIAM J. Appl. Dyn. Syst. 15, No. 4, 2109--2142 (2016; Zbl 1362.35208) Full Text: DOI arXiv
Albanez, Débora A. F.; Nussenzveig Lopes, Helena J.; Titi, Edriss S. Continuous data assimilation for the three-dimensional Navier-Stokes-\(\alpha\) model. (English) Zbl 1344.35078 Asymptotic Anal. 97, No. 1-2, 139-164 (2016). MSC: 35Q30 76D05 PDFBibTeX XMLCite \textit{D. A. F. Albanez} et al., Asymptotic Anal. 97, No. 1--2, 139--164 (2016; Zbl 1344.35078) Full Text: DOI arXiv
Li, Jinkai; Titi, Edriss S. Global well-posedness of the 2D Boussinesq equations with vertical dissipation. (English) Zbl 1336.35297 Arch. Ration. Mech. Anal. 220, No. 3, 983-1001 (2016). MSC: 35Q35 76D05 PDFBibTeX XMLCite \textit{J. Li} and \textit{E. S. Titi}, Arch. Ration. Mech. Anal. 220, No. 3, 983--1001 (2016; Zbl 1336.35297) Full Text: DOI arXiv
Farhat, Aseel; Lunasin, Evelyn; Titi, Edriss S. Abridged continuous data assimilation for the 2D Navier-Stokes equations utilizing measurements of only one component of the velocity field. (English) Zbl 1334.35202 J. Math. Fluid Mech. 18, No. 1, 1-23 (2016). MSC: 35Q30 93C20 37C50 76B75 34D06 PDFBibTeX XMLCite \textit{A. Farhat} et al., J. Math. Fluid Mech. 18, No. 1, 1--23 (2016; Zbl 1334.35202) Full Text: DOI arXiv
Mondaini, Cecilia F.; Titi, Edriss S. Postprocessing Galerkin method applied to a data assimilation algorithm: a uniform in time error estimate. arXiv:1612.06998 Preprint, arXiv:1612.06998 [math.NA] (2016). MSC: 35Q30 37L65 65M15 65M70 76B75 93C20 BibTeX Cite \textit{C. F. Mondaini} and \textit{E. S. Titi}, ``Postprocessing Galerkin method applied to a data assimilation algorithm: a uniform in time error estimate'', Preprint, arXiv:1612.06998 [math.NA] (2016) Full Text: arXiv OA License
Li, Jinkai; Titi, Edriss S. Recent Advances Concerning Certain Class of Geophysical Flows. arXiv:1604.01695 Preprint, arXiv:1604.01695 [math.AP] (2016). MSC: 35A01 35B45 35Q30 35Q86 76D03 76D09 BibTeX Cite \textit{J. Li} and \textit{E. S. Titi}, ``Recent Advances Concerning Certain Class of Geophysical Flows'', Preprint, arXiv:1604.01695 [math.AP] (2016) Full Text: arXiv OA License
Constantin, Peter (ed.); Friedlander, Susan (ed.); Seregin, Gregory A. (ed.); Titi, Edriss S. (ed.) Mathematical aspects of hydrodynamics. Abstracts from the workshop held August 9–15, 2015. (English) Zbl 1380.00057 Oberwolfach Rep. 12, No. 3, 2125-2187 (2015). MSC: 00B05 00B25 76-06 35-06 76Bxx 76Dxx 76Fxx 76W05 35Q30 35Q35 PDFBibTeX XMLCite \textit{P. Constantin} (ed.) et al., Oberwolfach Rep. 12, No. 3, 2125--2187 (2015; Zbl 1380.00057) Full Text: DOI
Lopes Filho, Milton C.; Nussenzveig Lopes, Helena J.; Titi, Edriss S.; Zang, Aibin Approximation of 2D Euler equations by the second-grade fluid equations with Dirichlet boundary conditions. (English) Zbl 1328.35153 J. Math. Fluid Mech. 17, No. 2, 327-340 (2015). MSC: 35Q30 76D05 76D10 76A10 35Q31 PDFBibTeX XMLCite \textit{M. C. Lopes Filho} et al., J. Math. Fluid Mech. 17, No. 2, 327--340 (2015; Zbl 1328.35153) Full Text: DOI arXiv
Hamed, Mohammad Abu; Guo, Yanqiu; Titi, Edriss S. Inertial manifolds for certain subgrid-scale \(\alpha\)-models of turbulence. (English) Zbl 1328.35150 SIAM J. Appl. Dyn. Syst. 14, No. 3, 1308-1325 (2015). Reviewer: Kai Schneider (Marseille) MSC: 35Q30 37L30 76B03 76F20 76F55 76F65 76D05 PDFBibTeX XMLCite \textit{M. A. Hamed} et al., SIAM J. Appl. Dyn. Syst. 14, No. 3, 1308--1325 (2015; Zbl 1328.35150) Full Text: DOI arXiv
Bessaih, Hakima; Olson, Eric; Titi, Edriss S. Continuous data assimilation with stochastically noisy data. (English) Zbl 1308.35161 Nonlinearity 28, No. 3, 729-753 (2015). MSC: 35Q30 60H15 60H30 76B75 93C20 34D06 PDFBibTeX XMLCite \textit{H. Bessaih} et al., Nonlinearity 28, No. 3, 729--753 (2015; Zbl 1308.35161) Full Text: DOI arXiv
Larios, Adam; Petersen, Mark; Titi, Edriss S.; Wingate, Beth A Computational Investigation of the Finite-Time Blow-Up of the 3D Incompressible Euler Equations Based on the Voigt Regularization. arXiv:1512.07877 Preprint, arXiv:1512.07877 [math.AP] (2015). MSC: 35Q30 76A10 76B03 76D03 76F20 76F55 76F65 76W05 BibTeX Cite \textit{A. Larios} et al., ``A Computational Investigation of the Finite-Time Blow-Up of the 3D Incompressible Euler Equations Based on the Voigt Regularization'', Preprint, arXiv:1512.07877 [math.AP] (2015) Full Text: arXiv OA License
Larios, Adam; Titi, Edriss S. A Blow-Up Criterion for the 3D Euler Equations Via the Euler-Voigt Inviscid Regularization. arXiv:1507.08203 Preprint, arXiv:1507.08203 [math.AP] (2015). MSC: 35B44 35A01 35Q30 35Q31 35Q35 76B03 BibTeX Cite \textit{A. Larios} and \textit{E. S. Titi}, ``A Blow-Up Criterion for the 3D Euler Equations Via the Euler-Voigt Inviscid Regularization'', Preprint, arXiv:1507.08203 [math.AP] (2015) Full Text: arXiv OA License
Larios, Adam; Titi, Edriss S. Higher-order global regularity of an inviscid Voigt-regularization of the three-dimensional inviscid resistive magnetohydrodynamic equations. (English) Zbl 1307.76083 J. Math. Fluid Mech. 16, No. 1, 59-76 (2014). MSC: 76W05 76B03 76D03 35B44 76A10 76A05 PDFBibTeX XMLCite \textit{A. Larios} and \textit{E. S. Titi}, J. Math. Fluid Mech. 16, No. 1, 59--76 (2014; Zbl 1307.76083) Full Text: DOI arXiv
Lopes Filho, Milton C.; Mazzucato, Anna L.; Niu, Dongjuan; Lopes, Helena J. Nussenzveig; Titi, Edriss S. Planar limits of three-dimensional incompressible flows with helical symmetry. (English) Zbl 1312.35144 J. Dyn. Differ. Equations 26, No. 4, 843-869 (2014). Reviewer: Cheng He (Beijing) MSC: 35Q35 65M70 76D05 PDFBibTeX XMLCite \textit{M. C. Lopes Filho} et al., J. Dyn. Differ. Equations 26, No. 4, 843--869 (2014; Zbl 1312.35144) Full Text: DOI arXiv
Azouani, Abderrahim; Titi, Edriss S. Feedback control of nonlinear dissipative systems by finite determining parameters – a reaction-diffusion paradigm. (English) Zbl 1304.35715 Evol. Equ. Control Theory 3, No. 4, 579-594 (2014). MSC: 35Q93 35K57 37L25 37L30 37N35 93B52 93C20 93D15 76D05 PDFBibTeX XMLCite \textit{A. Azouani} and \textit{E. S. Titi}, Evol. Equ. Control Theory 3, No. 4, 579--594 (2014; Zbl 1304.35715) Full Text: DOI arXiv
Biswas, A.; Jolly, M. S.; Martinez, V. R.; Titi, E. S. Dissipation length scale estimates for turbulent flows: a Wiener algebra approach. (English) Zbl 1300.35066 J. Nonlinear Sci. 24, No. 3, 441-471 (2014). MSC: 35Q30 76F02 76D05 PDFBibTeX XMLCite \textit{A. Biswas} et al., J. Nonlinear Sci. 24, No. 3, 441--471 (2014; Zbl 1300.35066) Full Text: DOI arXiv
Foias, C.; Jolly, M. S.; Kravchenko, R.; Titi, E. S. A unified approach to determining forms for the 2D Navier-Stokes equations – the general interpolants case. (English. Russian original) Zbl 1301.35108 Russ. Math. Surv. 69, No. 2, 359-381 (2014); translation from Usp. Mat. Nauk 69, No. 2, 177-200 (2014). Reviewer: Vladimir Mityushev (Kraków) MSC: 35Q35 76D05 35B41 PDFBibTeX XMLCite \textit{C. Foias} et al., Russ. Math. Surv. 69, No. 2, 359--381 (2014; Zbl 1301.35108); translation from Usp. Mat. Nauk 69, No. 2, 177--200 (2014) Full Text: DOI arXiv
Azouani, Abderrahim; Olson, Eric; Titi, Edriss S. Continuous data assimilation using general interpolant observables. (English) Zbl 1291.35168 J. Nonlinear Sci. 24, No. 2, 277-304 (2014). MSC: 35Q30 93C20 37C50 76B75 34D06 PDFBibTeX XMLCite \textit{A. Azouani} et al., J. Nonlinear Sci. 24, No. 2, 277--304 (2014; Zbl 1291.35168) Full Text: DOI arXiv
Biferale, Luca; Titi, Edriss S. On the global regularity of a helical-decimated version of the 3D Navier-Stokes equations. (English) Zbl 1275.35057 J. Stat. Phys. 151, No. 6, 1089-1098 (2013). MSC: 35B65 35A01 76D05 35Q30 35A02 PDFBibTeX XMLCite \textit{L. Biferale} and \textit{E. S. Titi}, J. Stat. Phys. 151, No. 6, 1089--1098 (2013; Zbl 1275.35057) Full Text: DOI arXiv
Bardos, Claude; Titi, Edriss S. Mathematics and Turbulence: where do we stand? arXiv:1301.0273 Preprint, arXiv:1301.0273 [math.AP] (2013). MSC: 35Q30 35Q31 76D03 76D09 BibTeX Cite \textit{C. Bardos} and \textit{E. S. Titi}, ``Mathematics and Turbulence: where do we stand?'', Preprint, arXiv:1301.0273 [math.AP] (2013) Full Text: DOI arXiv OA License
Constantin, Peter (ed.); Friedlander, Susan (ed.); Seregin, Gregory A. (ed.); Titi, Edriss S. (ed.) Mathematical aspects of hydrodynamics. Abstracts from the workshop held August 12–18, 2012. (English) Zbl 1349.00117 Oberwolfach Rep. 9, No. 3, 2389-2427 (2012). MSC: 00B05 00B25 76-06 76D05 35Q30 35Q31 35Q35 PDFBibTeX XMLCite \textit{P. Constantin} (ed.) et al., Oberwolfach Rep. 9, No. 3, 2389--2427 (2012; Zbl 1349.00117) Full Text: DOI
Foias, Ciprian; Jolly, Michael S.; Kravchenko, Rostyslav; Titi, Edriss S. A determining form for the two-dimensional Navier-Stokes equations: the Fourier modes case. (English) Zbl 1426.76103 J. Math. Phys. 53, No. 11, 115623, 30 p. (2012). MSC: 76D05 35Q30 PDFBibTeX XMLCite \textit{C. Foias} et al., J. Math. Phys. 53, No. 11, 115623, 30 p. (2012; Zbl 1426.76103) Full Text: DOI arXiv Link
Cao, Chongsheng; Titi, Edriss S. Global regularity criterion for the 3D Navier-Stokes equations involving one entry of the velocity gradient tensor. (English) Zbl 1256.35051 Arch. Ration. Mech. Anal. 202, No. 3, 919-932 (2011). MSC: 35Q30 76D03 35D35 PDFBibTeX XMLCite \textit{C. Cao} and \textit{E. S. Titi}, Arch. Ration. Mech. Anal. 202, No. 3, 919--932 (2011; Zbl 1256.35051) Full Text: DOI arXiv
Hayden, Kevin; Olson, Eric; Titi, Edriss S. Discrete data assimilation in the Lorenz and 2D Navier-Stokes equations. (English) Zbl 1302.76048 Physica D 240, No. 18, 1416-1425 (2011). MSC: 76D03 35Q30 37N10 PDFBibTeX XMLCite \textit{K. Hayden} et al., Physica D 240, No. 18, 1416--1425 (2011; Zbl 1302.76048) Full Text: DOI arXiv
Bardos, Claude; Frisch, Uriel; Pauls, Walter; Ray, Samriddhi Sankar; Titi, Edriss S. Entire solutions of hydrodynamical equations with exponential dissipation. (English) Zbl 1208.35100 Commun. Math. Phys. 293, No. 2, 519-543 (2010). MSC: 35Q30 35Q53 76D05 35B10 35A27 PDFBibTeX XMLCite \textit{C. Bardos} et al., Commun. Math. Phys. 293, No. 2, 519--543 (2010; Zbl 1208.35100) Full Text: DOI arXiv
Ramos, Fabio; Titi, Edriss S. Invariant measures for the 3D Navier-Stokes-Voigt equations and their Navier-Stokes limit. (English) Zbl 1387.35462 Discrete Contin. Dyn. Syst. 28, No. 1, 375-403 (2010). MSC: 35Q30 37L40 76A10 76D05 76D06 76M35 76F55 PDFBibTeX XMLCite \textit{F. Ramos} and \textit{E. S. Titi}, Discrete Contin. Dyn. Syst. 28, No. 1, 375--403 (2010; Zbl 1387.35462) Full Text: DOI arXiv
Cao, Yanping; Titi, Edriss S. On the rate of convergence of the two-dimensional \(\alpha \)-models of turbulence to the Navier-Stokes equations. (English) Zbl 1192.35129 Numer. Funct. Anal. Optim. 30, No. 11-12, 1231-1271 (2009). Reviewer: Nicolae Pop (Baia Mare) MSC: 35Q30 35A30 65M12 65M15 76D05 76F65 PDFBibTeX XMLCite \textit{Y. Cao} and \textit{E. S. Titi}, Numer. Funct. Anal. Optim. 30, No. 11--12, 1231--1271 (2009; Zbl 1192.35129) Full Text: DOI arXiv
Kalantarov, Varga K.; Levant, Boris; Titi, Edriss S. Gevrey regularity for the attractor of the 3D Navier-Stokes-Voight equations. (English) Zbl 1177.35152 J. Nonlinear Sci. 19, No. 2, 133-152 (2009). MSC: 35Q30 35B40 35B41 76F20 76F55 35P05 PDFBibTeX XMLCite \textit{V. K. Kalantarov} et al., J. Nonlinear Sci. 19, No. 2, 133--152 (2009; Zbl 1177.35152) Full Text: DOI arXiv
Bennis, Anne-Claire; Lewandowski, Roger; Titi, Edriss S. Simulations of turbulent ocean flow using a deconvolution model. (Simulations de l’écoulement turbulent marin avec un modèle de déconvolution.) (French. Abridged English version) Zbl 1159.76018 C. R., Math., Acad. Sci. Paris 347, No. 7-8, 445-450 (2009). MSC: 76F65 76M10 76D05 86A05 PDFBibTeX XMLCite \textit{A.-C. Bennis} et al., C. R., Math., Acad. Sci. Paris 347, No. 7--8, 445--450 (2009; Zbl 1159.76018) Full Text: DOI arXiv
Olson, Eric; Titi, Edriss S. Determining modes and Grashof number in 2D turbulence: a numerical case study. (English) Zbl 1178.76190 Theor. Comput. Fluid Dyn. 22, No. 5, 327-339 (2008). MSC: 76F35 76D05 76M22 PDFBibTeX XMLCite \textit{E. Olson} and \textit{E. S. Titi}, Theor. Comput. Fluid Dyn. 22, No. 5, 327--339 (2008; Zbl 1178.76190) Full Text: DOI
Ilyin, Alexei A.; Titi, Edriss S. The damped-driven 2D Navier-Stokes system on large elongated domains. (English) Zbl 1162.76323 J. Math. Fluid Mech. 10, No. 2, 159-175 (2008). MSC: 76D03 35Q30 PDFBibTeX XMLCite \textit{A. A. Ilyin} and \textit{E. S. Titi}, J. Math. Fluid Mech. 10, No. 2, 159--175 (2008; Zbl 1162.76323) Full Text: DOI
Cao, Chongsheng; Titi, Edriss S. Regularity criteria for the three-dimensional Navier-Stokes equations. (English) Zbl 1159.35053 Indiana Univ. Math. J. 57, No. 6, 2643-2661 (2008). MSC: 35Q30 76D05 76D03 PDFBibTeX XMLCite \textit{C. Cao} and \textit{E. S. Titi}, Indiana Univ. Math. J. 57, No. 6, 2643--2661 (2008; Zbl 1159.35053) Full Text: DOI arXiv Link
Cao, Chongsheng; Qin, Junlin; Titi, Edriss S. Regularity criterion for solutions of three-dimensional turbulent channel flows. (English) Zbl 1151.76012 Commun. Partial Differ. Equations 33, No. 3, 419-428 (2008). MSC: 76F02 35B65 35Q35 76D03 76D05 PDFBibTeX XMLCite \textit{C. Cao} et al., Commun. Partial Differ. Equations 33, No. 3, 419--428 (2008; Zbl 1151.76012) Full Text: DOI arXiv
Lunasin, Evelyn M.; Kurien, Susan; Taylor, Mark Alan; Titi, Edriss Saleh A study of the Navier-Stokes-\(\alpha\) model for two-dimensional turbulence. (English) Zbl 1273.76115 J. Turbul. 8, Paper No. 30, 21 p. (2007). MSC: 76F02 76D05 PDFBibTeX XMLCite \textit{E. M. Lunasin} et al., J. Turbul. 8, Paper No. 30, 21 p. (2007; Zbl 1273.76115) Full Text: DOI arXiv
Chernyshenko, Sergei I.; Constantin, Peter; Robinson, James C.; Titi, Edriss S. A posteriori regularity of the three-dimensional Navier-Stokes equations from numerical computations. (English) Zbl 1144.81329 J. Math. Phys. 48, No. 6, 065204, 15 p. (2007). MSC: 35Q30 35B65 65M60 76D05 PDFBibTeX XMLCite \textit{S. I. Chernyshenko} et al., J. Math. Phys. 48, No. 6, 065204, 15 p. (2007; Zbl 1144.81329) Full Text: DOI arXiv
Bardos, C.; Titi, E. S. Euler equations for incompressible ideal fluids. (English. Russian original) Zbl 1139.76010 Russ. Math. Surv. 62, No. 3, 409-451 (2007); translation from Usp. Mat. Nauk 62, No. 3, 5-46 (2007). MSC: 76B03 76F06 76-02 35Q30 PDFBibTeX XMLCite \textit{C. Bardos} and \textit{E. S. Titi}, Russ. Math. Surv. 62, No. 3, 409--451 (2007; Zbl 1139.76010); translation from Usp. Mat. Nauk 62, No. 3, 5--46 (2007) Full Text: DOI arXiv
Vishik, M. I.; Titi, E. S.; Chepyzhov, V. V. On convergence of trajectory attractors of the 3D Navier-Stokes-\(\alpha \) model as \(\alpha \) approaches 0. (English. Russian original) Zbl 1137.37037 Sb. Math. 198, No. 12, 1703-1736 (2007); translation from Mat. Sb. 198, No. 12, 3-26 (2007). MSC: 37L30 35Q30 35B41 76D05 37N10 76F02 PDFBibTeX XMLCite \textit{M. I. Vishik} et al., Sb. Math. 198, No. 12, 1703--1736 (2007; Zbl 1137.37037); translation from Mat. Sb. 198, No. 12, 3--26 (2007) Full Text: DOI
Constantin, Peter; Levant, Boris; Titi, Edriss S. Sharp lower bounds for the dimension of the global attractor of the Sabra shell model of turbulence. (English) Zbl 1115.76025 J. Stat. Phys. 127, No. 6, 1173-1192 (2007). MSC: 76D05 76F20 35Q30 35B41 PDFBibTeX XMLCite \textit{P. Constantin} et al., J. Stat. Phys. 127, No. 6, 1173--1192 (2007; Zbl 1115.76025) Full Text: DOI arXiv
Constantin, P.; Fefferman, C.; Titi, E. S.; Zarnescu, A. Regularity of coupled two-dimensional nonlinear Fokker-Planck and Navier-Stokes systems. (English) Zbl 1123.35043 Commun. Math. Phys. 270, No. 3, 789-811 (2007). Reviewer: Boris V. Loginov (Ul’yanovsk) MSC: 35Q35 76T20 76D05 82C70 PDFBibTeX XMLCite \textit{P. Constantin} et al., Commun. Math. Phys. 270, No. 3, 789--811 (2007; Zbl 1123.35043) Full Text: DOI arXiv
Olson, Eric; Titi, Edriss S. Viscosity versus vorticity stretching: global well-posedness for a family of Navier-Stokes-alpha-like models. (English) Zbl 1110.76011 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 66, No. 11, 2427-2458 (2007). MSC: 76D03 35Q30 PDFBibTeX XMLCite \textit{E. Olson} and \textit{E. S. Titi}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 66, No. 11, 2427--2458 (2007; Zbl 1110.76011) Full Text: DOI
Cao, Yanping; Lunasin, Evelyn M.; Titi, Edriss S. Global well-posedness of the three-dimensional viscous and inviscid simplified Bardina turbulence models. (English) Zbl 1127.35034 Commun. Math. Sci. 4, No. 4, 823-848 (2006). Reviewer: Bruno Scarpellini (Basel) MSC: 35Q30 37L30 76D03 35D05 76F20 76F55 76F65 76B03 PDFBibTeX XMLCite \textit{Y. Cao} et al., Commun. Math. Sci. 4, No. 4, 823--848 (2006; Zbl 1127.35034) Full Text: DOI arXiv
Ilyin, A. A.; Titi, E. S. Sharp estimates for the number of degrees of freedom for the damped-driven 2-D Navier-Stokes equations. (English) Zbl 1106.35049 J. Nonlinear Sci. 16, No. 3, 233-253 (2006). MSC: 35Q30 76D05 86A05 86A10 76D03 37L30 PDFBibTeX XMLCite \textit{A. A. Ilyin} and \textit{E. S. Titi}, J. Nonlinear Sci. 16, No. 3, 233--253 (2006; Zbl 1106.35049) Full Text: DOI arXiv
Constantin, Peter; Levant, Boris; Titi, Edriss S. Analytic study of shell models of turbulence. (English) Zbl 1113.34044 Physica D 219, No. 2, 120-141 (2006). Reviewer: Marianne Reichert (Frankfurt / Main) MSC: 34G20 76D05 34A45 PDFBibTeX XMLCite \textit{P. Constantin} et al., Physica D 219, No. 2, 120--141 (2006; Zbl 1113.34044) Full Text: DOI arXiv
Ilyin, Alexei A.; Lunasin, Evelyn M.; Titi, Edriss S. A modified-Leray-\(\alpha\) subgrid scale model of turbulence. (English) Zbl 1106.35050 Nonlinearity 19, No. 4, 879-897 (2006). MSC: 35Q30 76D03 76F20 76F55 76F65 37L30 PDFBibTeX XMLCite \textit{A. A. Ilyin} et al., Nonlinearity 19, No. 4, 879--897 (2006; Zbl 1106.35050) Full Text: DOI Link
Cheskidov, Alexey; Holm, Darryl D.; Olson, Eric; Titi, Edriss S. On a Leray-\(\alpha\) model of turbulence. (English) Zbl 1145.76386 Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 461, No. 2055, 629-649 (2005). MSC: 76F02 35Q35 37L30 37N10 76D05 PDFBibTeX XMLCite \textit{A. Cheskidov} et al., Proc. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 461, No. 2055, 629--649 (2005; Zbl 1145.76386) Full Text: DOI
Ilyin, A. A.; Miranville, A.; Titi, E. S. Small viscosity sharp estimates for the global attractor of the 2D damped-driven Navier-Stokes equations. (English) Zbl 1084.35058 Commun. Math. Sci. 2, No. 3, 403-426 (2004). MSC: 35Q30 86A05 37L30 76D05 76U05 76E20 86A10 37N10 PDFBibTeX XMLCite \textit{A. A. Ilyin} et al., Commun. Math. Sci. 2, No. 3, 403--426 (2004; Zbl 1084.35058) Full Text: DOI
Foias, Ciprian; Holm, Darryl D.; Titi, Edriss S. The three dimensional viscous Camassa-Holm equations, and their relation to the Navier-Stokes equations and turbulence theory. (English) Zbl 0995.35051 J. Dyn. Differ. Equations 14, No. 1, 1-35 (2002). Reviewer: Thomas Sonar (Braunschweig) MSC: 35Q30 76D05 37L30 35B65 76D03 76F02 PDFBibTeX XMLCite \textit{C. Foias} et al., J. Dyn. Differ. Equations 14, No. 1, 1--35 (2002; Zbl 0995.35051) Full Text: DOI arXiv
Cao, Chongsheng; Kevrekidis, Ioannis G.; Titi, Edriss S. Numerical criterion for the stabilization of steady states of the Navier-Stokes equations. (English) Zbl 0997.35048 Indiana Univ. Math. J. 50, Spec. Iss., 37-96 (2001). Reviewer: Thomas Sonar (Braunschweig) MSC: 35Q30 93D15 76D05 PDFBibTeX XMLCite \textit{C. Cao} et al., Indiana Univ. Math. J. 50, 37--96 (2001; Zbl 0997.35048) Full Text: DOI
Foias, Ciprian; Holm, Darryl D.; Titi, Edriss S. The Navier-Stokes-alpha model of fluid turbulence. (English) Zbl 1037.76022 Physica D 152-153, 505-519 (2001). MSC: 76F02 76D05 76F65 PDFBibTeX XMLCite \textit{C. Foias} et al., Physica D 152--153, 505--519 (2001; Zbl 1037.76022) Full Text: DOI arXiv
Cao, Chongsheng; Rammaha, Mohammad A.; Titi, Edriss S. The Navier-Stokes equations on the rotating 2-D sphere: Gevrey regularity and asymptotic degrees of freedom. (English) Zbl 0928.35120 Z. Angew. Math. Phys. 50, No. 3, 341-360 (1999). Reviewer: V.A.Sava (Iaşi) MSC: 35Q30 76D05 76D03 76U05 86A10 PDFBibTeX XMLCite \textit{C. Cao} et al., Z. Angew. Math. Phys. 50, No. 3, 341--360 (1999; Zbl 0928.35120) Full Text: DOI
García-Archilla, Bosco; Novo, Julia; Titi, Edriss S. An approximate inertial manifolds approach to postprocessing the Galerkin method for the Navier-Stokes equations. (English) Zbl 0930.76063 Math. Comput. 68, No. 227, 893-911 (1999). MSC: 76M25 76D05 PDFBibTeX XMLCite \textit{B. García-Archilla} et al., Math. Comput. 68, No. 227, 893--911 (1999; Zbl 0930.76063) Full Text: DOI
Chen, Shiyi; Foias, Ciprian; Holm, Darryl D.; Olson, Eric; Titi, Edriss S. Camassa-Holm equations as a closure model for turbulent channel and pipe flow. (English) Zbl 1042.76525 Phys. Rev. Lett. 81, No. 24, 5338-5341 (1998). MSC: 76F02 76D05 PDFBibTeX XMLCite \textit{S. Chen} et al., Phys. Rev. Lett. 81, No. 24, 5338--5341 (1998; Zbl 1042.76525) Full Text: DOI arXiv Link
Gibbon, J. D.; Titi, E. S. Attractor dimension and small length scale estimates for the three-dimensional Navier-Stokes equations. (English) Zbl 0906.35069 Nonlinearity 10, No. 1, 109-119 (1997). MSC: 35Q30 37C70 76D05 60E15 PDFBibTeX XMLCite \textit{J. D. Gibbon} and \textit{E. S. Titi}, Nonlinearity 10, No. 1, 109--119 (1997; Zbl 0906.35069) Full Text: DOI
Constantin, Peter; Doering, Charles R.; Titi, Edriss S. Rigorous estimates of small scales in turbulent flows. (English) Zbl 0862.35083 J. Math. Phys. 37, No. 12, 6152-6156 (1996). MSC: 35Q30 76D05 76F05 PDFBibTeX XMLCite \textit{P. Constantin} et al., J. Math. Phys. 37, No. 12, 6152--6156 (1996; Zbl 0862.35083) Full Text: DOI
Doering, Charles R.; Titi, Edriss S. Exponential decay rate of the power spectrum for solutions of the Navier-Stokes equations. (English) Zbl 1023.76513 Phys. Fluids 7, No. 6, 1384-1390 (1995). MSC: 76D03 76D05 35Q30 PDFBibTeX XMLCite \textit{C. R. Doering} and \textit{E. S. Titi}, Phys. Fluids 7, No. 6, 1384--1390 (1995; Zbl 1023.76513) Full Text: DOI
Constantin, Peter; E, Weinan; Titi, Edriss S. Onsager’s conjecture on the energy conservation for solutions of Euler’s equation. (English) Zbl 0818.35085 Commun. Math. Phys. 165, No. 1, 207-209 (1994). MSC: 35Q31 76D05 PDFBibTeX XMLCite \textit{P. Constantin} et al., Commun. Math. Phys. 165, No. 1, 207--209 (1994; Zbl 0818.35085) Full Text: DOI Backlinks: MO
Jones, D. A.; Titi, E. S. A remark on quasi-stationary approximate inertial manifolds for the Navier-Stokes equations. (English) Zbl 0808.35102 SIAM J. Math. Anal. 25, No. 3, 894-914 (1994). MSC: 35Q30 65N30 76D05 65M99 65N99 PDFBibTeX XMLCite \textit{D. A. Jones} and \textit{E. S. Titi}, SIAM J. Math. Anal. 25, No. 3, 894--914 (1994; Zbl 0808.35102) Full Text: DOI
Jones, Don A.; Titi, Edriss S. Upper bounds on the number of determining modes, nodes, and volume elements for the Navier-Stokes equations. (English) Zbl 0796.35128 Indiana Univ. Math. J. 42, No. 3, 875-887 (1993). Reviewer: Edriss S.Titi (Irvine) MSC: 35Q30 76D05 76F99 PDFBibTeX XMLCite \textit{D. A. Jones} and \textit{E. S. Titi}, Indiana Univ. Math. J. 42, No. 3, 875--887 (1993; Zbl 0796.35128) Full Text: DOI
Devulder, Christophe; Marion, Martine; Titi, Edriss S. On the rate of convergence of the nonlinear Galerkin methods. (English) Zbl 0783.65053 Math. Comput. 60, No. 202, 495-514 (1993). Reviewer: J.Albrycht (Poznań) MSC: 65J15 65N30 34G20 35Q30 76D05 PDFBibTeX XMLCite \textit{C. Devulder} et al., Math. Comput. 60, No. 202, 495--514 (1993; Zbl 0783.65053) Full Text: DOI
Mahalov, A.; Titi, E. S.; Leibovich, S. Invariant helical subspaces for the Navier-Stokes equations. (English) Zbl 0708.76044 Arch. Ration. Mech. Anal. 112, No. 3, 193-222 (1990). MSC: 76D05 35Q30 PDFBibTeX XMLCite \textit{A. Mahalov} et al., Arch. Ration. Mech. Anal. 112, No. 3, 193--222 (1990; Zbl 0708.76044) Full Text: DOI
Titi, Edriss Saleh On a criterion for locating stable stationary solutions to the Navier- Stokes equations. (English) Zbl 0642.76031 Nonlinear Anal., Theory Methods Appl. 11, 1085-1102 (1987). Reviewer: A.Pil’kevich MSC: 76D05 35Q30 PDFBibTeX XMLCite \textit{E. S. Titi}, Nonlinear Anal., Theory Methods Appl. 11, 1085--1102 (1987; Zbl 0642.76031) Full Text: DOI