Farwig, Reinhard \(L^s(L^q)\)-estimates of the pressure – the proof of Sohr-von Wahl and its impact on mathematical fluid dynamics. (English) Zbl 07780309 Arch. Math. 121, No. 5-6, 643-657 (2023). Reviewer: Gelu Paşa (Bucureşti) MSC: 35Q30 35-03 35B65 76D07 76D05 35D30 PDFBibTeX XMLCite \textit{R. Farwig}, Arch. Math. 121, No. 5--6, 643--657 (2023; Zbl 07780309) Full Text: DOI OA License
Farwig, Reinhard; Tsuda, Kazuyuki The Fujita-Kato approach for the Navier-Stokes equations with moving boundary and its application. (English) Zbl 1493.35065 J. Math. Fluid Mech. 24, No. 3, Paper No. 77, 26 p. (2022). MSC: 35Q30 35B10 76D05 PDFBibTeX XMLCite \textit{R. Farwig} and \textit{K. Tsuda}, J. Math. Fluid Mech. 24, No. 3, Paper No. 77, 26 p. (2022; Zbl 1493.35065) Full Text: DOI
Farwig, Reinhard From Jean Leray to the millennium problem: the Navier-Stokes equations. (English) Zbl 1492.35002 J. Evol. Equ. 21, No. 3, 3243-3263 (2021); correction ibid. 21, No. 3, 3265-3266 (2021). Reviewer: Evan Miller (Hamilton) MSC: 35-02 35Q30 76D05 35B65 35B44 PDFBibTeX XMLCite \textit{R. Farwig}, J. Evol. Equ. 21, No. 3, 3243--3263 (2021; Zbl 1492.35002) Full Text: DOI
Farwig, Reinhard; Schmidt, Andreas An \(L^2\) approach to viscous flow in the half space with free elastic surface. (English) Zbl 1479.35608 J. Elliptic Parabol. Equ. 7, No. 2, 601-621 (2021). MSC: 35Q30 35L30 35D35 35A01 74K20 42A38 76D05 35R35 PDFBibTeX XMLCite \textit{R. Farwig} and \textit{A. Schmidt}, J. Elliptic Parabol. Equ. 7, No. 2, 601--621 (2021; Zbl 1479.35608) Full Text: DOI
Farwig, Reinhard; Kanamaru, Ryo Optimality of Serrin type extension criteria to the Navier-Stokes equations. (English) Zbl 1473.35400 Adv. Nonlinear Anal. 10, 1071-1085 (2021). MSC: 35Q30 35B65 46E35 76D05 35D35 PDFBibTeX XMLCite \textit{R. Farwig} and \textit{R. Kanamaru}, Adv. Nonlinear Anal. 10, 1071--1085 (2021; Zbl 1473.35400) Full Text: DOI
Farwig, Reinhard The millennium problem of the Navier-Stokes equations. (Das Millenniumsproblem der Navier-Stokes-Gleichungen.) (German) Zbl 1448.35362 Mitt. Dtsch. Math.-Ver. 28, No. 1, 18-25 (2020). Reviewer: Alain Brillard (Riedisheim) MSC: 35Q30 35A01 35A02 35B65 76D05 35-02 PDFBibTeX XMLCite \textit{R. Farwig}, Mitt. Dtsch. Math.-Ver. 28, No. 1, 18--25 (2020; Zbl 1448.35362) Full Text: DOI
Farwig, Reinhard; Qian, Chenyin; Zhang, Ping Incompressible inhomogeneous fluids in bounded domains of \(\mathbb{R}^3\) with bounded density. (English) Zbl 1433.35222 J. Funct. Anal. 278, No. 5, Article ID 108394, 36 p. (2020). MSC: 35Q30 35Q35 76D03 76D05 76D07 35D30 35B65 PDFBibTeX XMLCite \textit{R. Farwig} et al., J. Funct. Anal. 278, No. 5, Article ID 108394, 36 p. (2020; Zbl 1433.35222) Full Text: DOI
Farwig, Reinhard; Kozono, Hideo; Wegmann, David Maximal regularity of the Stokes operator in an exterior domain with moving boundary and application to the Navier-Stokes equations. (English) Zbl 1428.35286 Math. Ann. 375, No. 3-4, 949-972 (2019). MSC: 35Q30 35B40 35J65 76D05 76D07 35R37 35B65 76D03 PDFBibTeX XMLCite \textit{R. Farwig} et al., Math. Ann. 375, No. 3--4, 949--972 (2019; Zbl 1428.35286) Full Text: DOI
Farwig, Reinhard; Giga, Yoshikazu; Hsu, Pen-Yuan On the continuity of the solutions to the Navier-Stokes equations with initial data in critical Besov spaces. (English) Zbl 1428.35285 Ann. Mat. Pura Appl. (4) 198, No. 5, 1495-1511 (2019). MSC: 35Q30 76D05 35B35 35D35 35A01 35A02 PDFBibTeX XMLCite \textit{R. Farwig} et al., Ann. Mat. Pura Appl. (4) 198, No. 5, 1495--1511 (2019; Zbl 1428.35285) Full Text: DOI
Farwig, Reinhard; Schulz, Raphael; Taniuchi, Yasushi Spatial asymptotic profiles of solutions to the Navier-Stokes system in a rotating frame with fast decaying data. (English) Zbl 1401.76159 Hokkaido Math. J. 47, No. 3, 501-529 (2018). MSC: 76U05 76D05 35B40 35Q30 35Q35 PDFBibTeX XMLCite \textit{R. Farwig} et al., Hokkaido Math. J. 47, No. 3, 501--529 (2018; Zbl 1401.76159) Full Text: DOI
Danchin, Raphaël (ed.); Farwig, Reinhard (ed.); Neustupa, Jiří (ed.); Penel, Patrick (ed.) Mathematical analysis in fluid mechanics: selected recent results. International conference on vorticity, rotation and symmetry (IV) – complex fluids and the issue of regularity, CIRM, Luminy, Marseille, France, May 8–12, 2017. Proceedings. (English) Zbl 1396.35001 Contemporary Mathematics 710. Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-3646-9/pbk; 978-1-4704-4807-3/ebook). vi, 242 p. (2018). MSC: 35-06 35Q35 35Q30 76D05 76D07 76W05 00B25 PDFBibTeX XMLCite \textit{R. Danchin} (ed.) et al., Mathematical analysis in fluid mechanics: selected recent results. International conference on vorticity, rotation and symmetry (IV) -- complex fluids and the issue of regularity, CIRM, Luminy, Marseille, France, May 8--12, 2017. Proceedings. Providence, RI: American Mathematical Society (AMS) (2018; Zbl 1396.35001) Full Text: DOI
Farwig, Reinhard; Giga, Yoshikazu Well-chosen weak solutions of the instationary Navier-Stokes system and their uniqueness. (English) Zbl 1397.35170 Hokkaido Math. J. 47, No. 2, 373-385 (2018). Reviewer: Anthony D. Osborne (Keele) MSC: 35Q30 35B65 76D05 76D03 35D30 35D35 PDFBibTeX XMLCite \textit{R. Farwig} and \textit{Y. Giga}, Hokkaido Math. J. 47, No. 2, 373--385 (2018; Zbl 1397.35170) Full Text: DOI Euclid Link
Farwig, Reinhard; Giga, Yoshikazu; Hsu, Pen-Yuan The Navier-Stokes equations with initial values in Besov spaces of type \(B^{-1+3/q}_{q,\infty}\). (English) Zbl 1390.35229 J. Korean Math. Soc. 54, No. 5, 1483-1504 (2017). MSC: 35Q30 35A02 76D03 76D05 35D35 35D30 35B65 PDFBibTeX XMLCite \textit{R. Farwig} et al., J. Korean Math. Soc. 54, No. 5, 1483--1504 (2017; Zbl 1390.35229) Full Text: DOI
Wegmann, David; Farwig, Reinhard; Kozono, Hideo Decay of non-stationary Navier-Stokes flow with nonzero Dirichlet boundary data. (English) Zbl 1390.35238 Indiana Univ. Math. J. 66, No. 6, 2169-2185 (2017). Reviewer: Piotr Biler (Wrocław) MSC: 35Q30 76D05 35B40 35J65 PDFBibTeX XMLCite \textit{D. Wegmann} et al., Indiana Univ. Math. J. 66, No. 6, 2169--2185 (2017; Zbl 1390.35238) Full Text: DOI Link Link
Farwig, Reinhard Jean Leray: Sur le mouvement d’un liquide visqueux emplissant l’espace. Acta Math. 63 (1934), 193–248. (English) Zbl 1373.76004 Jahresber. Dtsch. Math.-Ver. 119, No. 4, 249-272 (2017). MSC: 76-03 76D05 01A70 PDFBibTeX XMLCite \textit{R. Farwig}, Jahresber. Dtsch. Math.-Ver. 119, No. 4, 249--272 (2017; Zbl 1373.76004) Full Text: DOI
Farwig, Reinhard; Kozono, Hideo; Wegmann, David Existence of strong solutions and decay of turbulent solutions of Navier-Stokes flow with nonzero Dirichlet boundary data. (English) Zbl 1367.35107 J. Math. Anal. Appl. 453, No. 1, 271-286 (2017). MSC: 35Q30 35D35 35D30 35B40 76D05 PDFBibTeX XMLCite \textit{R. Farwig} et al., J. Math. Anal. Appl. 453, No. 1, 271--286 (2017; Zbl 1367.35107) Full Text: DOI
Farwig, Reinhard; Giga, Yoshikazu; Hsu, Pen-Yuan Initial values for the Navier-Stokes equations in spaces with weights in time. (English) Zbl 1364.35236 Funkc. Ekvacioj, Ser. Int. 59, No. 2, 199-216 (2016). MSC: 35Q30 76D05 35D30 35D35 PDFBibTeX XMLCite \textit{R. Farwig} et al., Funkc. Ekvacioj, Ser. Int. 59, No. 2, 199--216 (2016; Zbl 1364.35236) Full Text: DOI Link
Riechwald, Paul Felix; Farwig, Reinhard Regularity criteria for weak solutions of the Navier-Stokes system in general unbounded domains. (English) Zbl 1342.35226 Discrete Contin. Dyn. Syst., Ser. S 9, No. 1, 157-172 (2016). MSC: 35Q30 35B65 76D05 35D30 PDFBibTeX XMLCite \textit{P. F. Riechwald} and \textit{R. Farwig}, Discrete Contin. Dyn. Syst., Ser. S 9, No. 1, 157--172 (2016; Zbl 1342.35226) Full Text: DOI
Farwig, Reinhard; Sohr, Hermann; Varnhorn, Werner Local strong solutions of the nonhomogeneous Navier-Stokes system with control of the interval of existence. (English) Zbl 1362.35207 Topol. Methods Nonlinear Anal. 46, No. 2, 999-1012 (2015). MSC: 35Q30 76D05 35D30 35D35 PDFBibTeX XMLCite \textit{R. Farwig} et al., Topol. Methods Nonlinear Anal. 46, No. 2, 999--1012 (2015; Zbl 1362.35207) Full Text: DOI
Farwig, Reinhard; Nakatsuka, Tomoyuki; Taniuchi, Yasushi Uniqueness of solutions on the whole time axis to the Navier-Stokes equations in unbounded domains. (English) Zbl 1334.35203 Commun. Partial Differ. Equations 40, No. 10, 1884-1904 (2015). Reviewer: Piotr Biler (Wroclaw) MSC: 35Q30 76D05 PDFBibTeX XMLCite \textit{R. Farwig} et al., Commun. Partial Differ. Equations 40, No. 10, 1884--1904 (2015; Zbl 1334.35203) Full Text: DOI
Farwig, Reinhard; Riechwald, Paul Felix Very weak solutions and the Fujita-Kato approach to the Navier-Stokes system in general unbounded domains. (English) Zbl 1333.35162 NoDEA, Nonlinear Differ. Equ. Appl. 22, No. 5, 1143-1165 (2015). Reviewer: Ruxandra Stavre (Bucureşti) MSC: 35Q30 35B65 76D05 76D03 35D30 PDFBibTeX XMLCite \textit{R. Farwig} and \textit{P. F. Riechwald}, NoDEA, Nonlinear Differ. Equ. Appl. 22, No. 5, 1143--1165 (2015; Zbl 1333.35162) Full Text: DOI
Ri, Myong-Hwan; Farwig, Reinhard Maximal regularity in exponentially weighted Lebesgue spaces of the Stokes operator in unbounded cylinders. (English) Zbl 1321.35140 Analysis, München 35, No. 3, 139-160 (2015). MSC: 35Q30 76D05 76D07 35B65 PDFBibTeX XMLCite \textit{M.-H. Ri} and \textit{R. Farwig}, Analysis, München 35, No. 3, 139--160 (2015; Zbl 1321.35140) Full Text: DOI arXiv
Farwig, Reinhard; Nakatsuka, Tomoyuki; Taniuchi, Yasushi Existence of solutions on the whole time axis to the Navier-Stokes equations with precompact range in \(L^3\). (English) Zbl 1321.35133 Arch. Math. 104, No. 6, 539-550 (2015). Reviewer: Mamadou Sy (Saint-Louis) MSC: 35Q30 35A01 76D05 PDFBibTeX XMLCite \textit{R. Farwig} et al., Arch. Math. 104, No. 6, 539--550 (2015; Zbl 1321.35133) Full Text: DOI
Farwig, Reinhard; Riechwald, Paul Felix Very weak solutions to the Navier-Stokes system in general unbounded domains. (English) Zbl 1328.35010 J. Evol. Equ. 15, No. 2, 253-279 (2015). MSC: 35B65 76D05 76D03 PDFBibTeX XMLCite \textit{R. Farwig} and \textit{P. F. Riechwald}, J. Evol. Equ. 15, No. 2, 253--279 (2015; Zbl 1328.35010) Full Text: DOI
Farwig, Reinhard; Sauer, Jonas Very weak solutions of the stationary Stokes equations in unbounded domains of half space type. (English) Zbl 1349.76055 Math. Bohem. 140, No. 1, 81-109 (2015). MSC: 76D05 35J65 76D07 35Q35 PDFBibTeX XMLCite \textit{R. Farwig} and \textit{J. Sauer}, Math. Bohem. 140, No. 1, 81--109 (2015; Zbl 1349.76055) Full Text: Link
Farwig, Reinhard On regularity of weak solutions to the instationary Navier-Stokes system: a review on recent results. (English) Zbl 1304.35484 Ann. Univ. Ferrara, Sez. VII, Sci. Mat. 60, No. 1, 91-122 (2014). Reviewer: Vladimir Mityushev (Kraków) MSC: 35Q30 35B65 76D05 76D03 35B44 35D30 35D35 PDFBibTeX XMLCite \textit{R. Farwig}, Ann. Univ. Ferrara, Sez. VII, Sci. Mat. 60, No. 1, 91--122 (2014; Zbl 1304.35484) Full Text: DOI
Farwig, Reinhard; Sohr, Hermann; Varnhorn, Werner Besov space regularity conditions for weak solutions of the Navier-Stokes equations. (English) Zbl 1291.35177 J. Math. Fluid Mech. 16, No. 2, 307-320 (2014). MSC: 35Q30 76D03 76D05 PDFBibTeX XMLCite \textit{R. Farwig} et al., J. Math. Fluid Mech. 16, No. 2, 307--320 (2014; Zbl 1291.35177) Full Text: DOI
Farwig, Reinhard; Kozono, Hideo Weak solutions of the Navier-Stokes equations with non-zero boundary values in an exterior domain satisfying the strong energy inequality. (English) Zbl 1285.35065 J. Differ. Equations 256, No. 7, 2633-2658 (2014). MSC: 35Q30 35J65 76D05 35D30 PDFBibTeX XMLCite \textit{R. Farwig} and \textit{H. Kozono}, J. Differ. Equations 256, No. 7, 2633--2658 (2014; Zbl 1285.35065) Full Text: DOI
Farwig, Reinhard; Guenther, Ronald B.; Thomann, Enrique A.; Nečasová, Šarka The fundamental solution of linearized nonstationary Navier-Stokes equations of motion around a rotating and translating body. (English) Zbl 1280.35087 Discrete Contin. Dyn. Syst. 34, No. 2, 511-529 (2014). Reviewer: Prabhat Kumar Mahanti (Saint John) MSC: 35Q30 76D05 76D07 PDFBibTeX XMLCite \textit{R. Farwig} et al., Discrete Contin. Dyn. Syst. 34, No. 2, 511--529 (2014; Zbl 1280.35087) Full Text: DOI
Farwig, Reinhard; Komo, Christian Optimal initial value conditions for local strong solutions of the Navier-Stokes equations in exterior domains. (English) Zbl 1274.76189 Analysis, München 33, No. 2, 101-120 (2013). MSC: 76D05 35Q30 35B65 PDFBibTeX XMLCite \textit{R. Farwig} and \textit{C. Komo}, Analysis, München 33, No. 2, 101--120 (2013; Zbl 1274.76189) Full Text: DOI
Farwig, Reinhard; Taniuchi, Yasushi Uniqueness of backward asymptotically almost periodic-in-time solutions to Navier-Stokes equations in unbounded domains. (English) Zbl 1260.35109 Discrete Contin. Dyn. Syst., Ser. S 6, No. 5, 1215-1224 (2013). MSC: 35Q30 35Q35 76D05 PDFBibTeX XMLCite \textit{R. Farwig} and \textit{Y. Taniuchi}, Discrete Contin. Dyn. Syst., Ser. S 6, No. 5, 1215--1224 (2013; Zbl 1260.35109) Full Text: DOI
Farwig, Reinhard; Sohr, Hermann; Varnhorn, Werner Extensions of Serrin’s uniqueness and regularity conditions for the Navier-Stokes equations. (English) Zbl 1254.76053 J. Math. Fluid Mech. 14, No. 3, 529-540 (2012). MSC: 76D05 35Q30 PDFBibTeX XMLCite \textit{R. Farwig} et al., J. Math. Fluid Mech. 14, No. 3, 529--540 (2012; Zbl 1254.76053) Full Text: DOI
Farwig, Reinhard; Morimoto, Hiroko Leray’s inequality for fluid flow in symmetric multi-connected two-dimensional domains. (English) Zbl 1256.35053 Tokyo J. Math. 35, No. 1, 63-70 (2012). Reviewer: Pablo Amster (Buenos Aires) MSC: 35Q30 76D05 35D30 35B06 PDFBibTeX XMLCite \textit{R. Farwig} and \textit{H. Morimoto}, Tokyo J. Math. 35, No. 1, 63--70 (2012; Zbl 1256.35053) Full Text: DOI Euclid
Farwig, R.; Kozono, H.; Sohr, H. Global Leray-Hopf weak solutions of the Navier-Stokes equations with nonzero time-dependent boundary values. (English) Zbl 1247.35090 Escher, Joachim (ed.) et al., Parabolic problems. The Herbert Amann Festschrift. Based on the conference on nonlinear parabolic problems held in celebration of Herbert Amann’s 70th birthday at the Banach Center in Bȩdlewo, Poland, May 10–16, 2009. Basel: Birkhäuser (ISBN 978-3-0348-0074-7/hbk; 978-3-0348-0075-4/ebook). Progress in Nonlinear Differential Equations and Their Applications 80, 211-232 (2011). MSC: 35Q30 35J65 76D05 35D30 PDFBibTeX XMLCite \textit{R. Farwig} et al., Prog. Nonlinear Differ. Equ. Appl. 80, 211--232 (2011; Zbl 1247.35090) Full Text: DOI
Farwig, Reinhard; Galdi, Giovanni P.; Kyed, Mads Asymptotic structure of a Leray solution to the Navier-Stokes flow around a rotating body. (English) Zbl 1234.35035 Pac. J. Math. 253, No. 2, 367-382 (2011). MSC: 35B40 35Q30 76U05 76D05 PDFBibTeX XMLCite \textit{R. Farwig} et al., Pac. J. Math. 253, No. 2, 367--382 (2011; Zbl 1234.35035) Full Text: DOI Link
Farwig, Reinhard; Taniuchi, Yasushi Uniqueness of almost periodic-in-time solutions to Navier-Stokes equations in unbounded domains. (English) Zbl 1231.35145 J. Evol. Equ. 11, No. 3, 485-508 (2011). MSC: 35Q30 35A02 35B09 76D05 PDFBibTeX XMLCite \textit{R. Farwig} and \textit{Y. Taniuchi}, J. Evol. Equ. 11, No. 3, 485--508 (2011; Zbl 1231.35145) Full Text: DOI
Farwig, Reinhard; Hishida, Toshiaki Leading term at infinity of steady Navier-Stokes flow around a rotating obstacle. (English) Zbl 1229.35173 Math. Nachr. 284, No. 16, 2065-2077 (2011). MSC: 35Q30 35B40 76D05 PDFBibTeX XMLCite \textit{R. Farwig} and \textit{T. Hishida}, Math. Nachr. 284, No. 16, 2065--2077 (2011; Zbl 1229.35173) Full Text: DOI
Farwig, Reinhard; Kozono, Hideo; Sohr, Hermann Global weak solutions of the Navier-Stokes equations with nonhomogeneous boundary data and divergence. (English) Zbl 1236.35103 Rend. Semin. Mat. Univ. Padova 125, 51-70 (2011). MSC: 35Q30 76D05 35J65 35D30 PDFBibTeX XMLCite \textit{R. Farwig} et al., Rend. Semin. Mat. Univ. Padova 125, 51--70 (2011; Zbl 1236.35103) Full Text: DOI EuDML Link
Farwig, Reinhard; Sohr, Hermann; Varnhorn, Werner Necessary and sufficient conditions on local strong solvability of the Navier-Stokes system. (English) Zbl 1209.35096 Appl. Anal. 90, No. 1-2, 47-58 (2011). MSC: 35Q30 76D05 76D03 PDFBibTeX XMLCite \textit{R. Farwig} et al., Appl. Anal. 90, No. 1--2, 47--58 (2011; Zbl 1209.35096) Full Text: DOI
Farwig, Reinhard; Kozono, Hideo; Sohr, Hermann Regularity of weak solutions for the Navier-Stokes equations via energy criteria. (English) Zbl 1374.35280 Rannacher, Rolf (ed.) et al., Advances in mathematical fluid mechanics. Dedicated to Giovanni Paolo Galdi on the occasion of his 60th birthday. Selected papers of the international conference on mathematical fluid mechanics, Estoril, Portugal, May 21–25, 2007. Berlin: Springer (ISBN 978-3-642-04067-2/hbk; 978-3-642-04068-9/ebook). 215-227 (2010). MSC: 35Q30 76D05 76D03 PDFBibTeX XMLCite \textit{R. Farwig} et al., in: Advances in mathematical fluid mechanics. Dedicated to Giovanni Paolo Galdi on the occasion of his 60th birthday. Selected papers of the international conference on mathematical fluid mechanics, Estoril, Portugal, May 21--25, 2007. Berlin: Springer. 215--227 (2010; Zbl 1374.35280) Full Text: DOI
Farwig, Reinhard; Okabe, Takahiro Periodic solutions of the Navier-Stokes equations with inhomogeneous boundary conditions. (English) Zbl 1205.35192 Ann. Univ. Ferrara, Sez. VII, Sci. Mat. 56, No. 2, 249-281 (2010). MSC: 35Q30 35B10 35D30 76D03 76D05 PDFBibTeX XMLCite \textit{R. Farwig} and \textit{T. Okabe}, Ann. Univ. Ferrara, Sez. VII, Sci. Mat. 56, No. 2, 249--281 (2010; Zbl 1205.35192) Full Text: DOI
Farwig, R.; Kozono, H.; Sohr, H. Global weak solutions of the Navier-Stokes system with nonzero boundary conditions. (English) Zbl 1291.35030 Funkc. Ekvacioj, Ser. Int. 53, No. 2, 231-247 (2010). MSC: 35D30 76D03 35Q30 76D05 PDFBibTeX XMLCite \textit{R. Farwig} et al., Funkc. Ekvacioj, Ser. Int. 53, No. 2, 231--247 (2010; Zbl 1291.35030) Full Text: DOI
Farwig, Reinhard; Taniuchi, Yasushi On the energy equality of Navier-Stokes equations in general unbounded domains. (English) Zbl 1202.35169 Arch. Math. 95, No. 5, 447-456 (2010). MSC: 35Q35 76D05 76D03 PDFBibTeX XMLCite \textit{R. Farwig} and \textit{Y. Taniuchi}, Arch. Math. 95, No. 5, 447--456 (2010; Zbl 1202.35169) Full Text: DOI
Farwig, Reinhard; Sohr, Hermann On the existence of local strong solutions for the Navier-Stokes equations in completely general domains. (English) Zbl 1194.35306 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 73, No. 6, 1459-1465 (2010). MSC: 35Q30 35B30 76D05 76D03 PDFBibTeX XMLCite \textit{R. Farwig} and \textit{H. Sohr}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 73, No. 6, 1459--1465 (2010; Zbl 1194.35306) Full Text: DOI
Farwig, Reinhard; Komo, Christian Regularity of weak solutions to the Navier-Stokes equations in exterior domains. (English) Zbl 1189.76115 NoDEA, Nonlinear Differ. Equ. Appl. 17, No. 3, 303-321 (2010). MSC: 76D05 35Q30 35B65 PDFBibTeX XMLCite \textit{R. Farwig} and \textit{C. Komo}, NoDEA, Nonlinear Differ. Equ. Appl. 17, No. 3, 303--321 (2010; Zbl 1189.76115) Full Text: DOI
Farwig, Reinhard; Hishida, Toshiaki Asymptotic profiles of steady Stokes and Navier-Stokes flows around a rotating obstacle. (English) Zbl 1205.35191 Ann. Univ. Ferrara, Sez. VII, Sci. Mat. 55, No. 2, 263-277 (2009). MSC: 35Q30 35Q35 35B40 76D05 76D07 PDFBibTeX XMLCite \textit{R. Farwig} and \textit{T. Hishida}, Ann. Univ. Ferrara, Sez. VII, Sci. Mat. 55, No. 2, 263--277 (2009; Zbl 1205.35191) Full Text: DOI
Farwig, R.; Sohr, H. Existence, uniqueness and regularity of stationary solutions to inhomogeneous Navier-Stokes equations in \(\mathbb R^n\). (English) Zbl 1224.76034 Czech. Math. J. 59, No. 1, 61-79 (2009). MSC: 76D05 35J65 35Q30 76D07 PDFBibTeX XMLCite \textit{R. Farwig} and \textit{H. Sohr}, Czech. Math. J. 59, No. 1, 61--79 (2009; Zbl 1224.76034) Full Text: DOI EuDML
Farwig, Reinhard; Kozono, Hideo; Sohr, Hermann Energy-based regularity criteria for the Navier-Stokes equations. (English) Zbl 1185.35162 J. Math. Fluid Mech. 11, No. 3, 428-442 (2009). MSC: 35Q30 76D03 76D05 35B65 35D30 PDFBibTeX XMLCite \textit{R. Farwig} et al., J. Math. Fluid Mech. 11, No. 3, 428--442 (2009; Zbl 1185.35162) Full Text: DOI
Farwig, Reinhard; Sohr, Hermann; Varnhorn, Werner On optimal initial value conditions for local strong solutions of the Navier-Stokes equations. (English) Zbl 1179.35210 Ann. Univ. Ferrara, Sez. VII, Sci. Mat. 55, No. 1, 89-110 (2009). MSC: 35Q30 76D05 PDFBibTeX XMLCite \textit{R. Farwig} et al., Ann. Univ. Ferrara, Sez. VII, Sci. Mat. 55, No. 1, 89--110 (2009; Zbl 1179.35210) Full Text: DOI
Farwig, Reinhard; Sohr, Hermann Optimal initial value conditions for the existence of local strong solutions of the Navier-Stokes equations. (English) Zbl 1173.35096 Math. Ann. 345, No. 3, 631-642 (2009). MSC: 35Q30 76D05 76D07 35D05 PDFBibTeX XMLCite \textit{R. Farwig} and \textit{H. Sohr}, Math. Ann. 345, No. 3, 631--642 (2009; Zbl 1173.35096) Full Text: DOI
Farwig, Reinhard; Kozono, Hideo; Sohr, Hermann Maximal regularity of the Stokes operator in general unbounded domains of \(\mathbb R^n\). (English) Zbl 1171.35448 Amann, Herbert (ed.) et al., Functional analysis and evolution equations. The Günter Lumer volume. Basel: Birkhäuser (ISBN 978-3-7643-7793-9/hbk). 257-272 (2008). MSC: 35Q35 76D05 35B65 76D03 47F05 PDFBibTeX XMLCite \textit{R. Farwig} et al., in: Functional analysis and evolution equations. The Günter Lumer volume. Basel: Birkhäuser. 257--272 (2008; Zbl 1171.35448)
Farwig, Reinhard; Kozono, Hideo; Sohr, Hermann Criteria of local in time regularity of the Navier-Stokes equations beyond Serrin’s condition. (English) Zbl 1154.35416 Rencławowicz, Joanna (ed.) et al., Parabolic and Navier-Stokes equations. Part 1. Proceedings of the confererence, Bȩdlewo, Poland, September 10–17, 2006. Warsaw: Polish Academy of Sciences, Institute of Mathematics. Banach Center Publications 81, Pt. 1, 175-184 (2008). MSC: 35Q30 35D10 35B65 76D05 76D03 PDFBibTeX XMLCite \textit{R. Farwig} et al., Banach Cent. Publ. 81, 175--184 (2008; Zbl 1154.35416) Full Text: Link
Farwig, Reinhard; Kozono, Hideo; Sohr, Hermann Local in time regularity properties of the Navier-Stokes equations. (English) Zbl 1175.35100 Indiana Univ. Math. J. 56, No. 5, 2111-2131 (2007). Reviewer: Bernard Ducomet (Bruyères le Châtel) MSC: 35Q30 76D05 35B65 PDFBibTeX XMLCite \textit{R. Farwig} et al., Indiana Univ. Math. J. 56, No. 5, 2111--2131 (2007; Zbl 1175.35100) Full Text: DOI
Farwig, Reinhard; Kozono, Hideo; Sohr, Hermann Very weak solutions of the Navier-Stokes equations in exterior domains with nonhomogeneous data. (English) Zbl 1107.76022 J. Math. Soc. Japan 59, No. 1, 127-150 (2007). MSC: 76D03 35Q30 76D05 PDFBibTeX XMLCite \textit{R. Farwig} et al., J. Math. Soc. Japan 59, No. 1, 127--150 (2007; Zbl 1107.76022) Full Text: DOI
Ri, Myong-Hwan; Farwig, Reinhard Existence and exponential stability in \(L^{r}\)-spaces of stationary Navier-Stokes flows with prescribed flux in infinite cylindrical domains. (English) Zbl 1127.35040 Math. Methods Appl. Sci. 30, No. 2, 171-199 (2007). Reviewer: Milan Pokorný (Praha) MSC: 35Q30 35B35 76D03 76D05 76D07 76E99 PDFBibTeX XMLCite \textit{M.-H. Ri} and \textit{R. Farwig}, Math. Methods Appl. Sci. 30, No. 2, 171--199 (2007; Zbl 1127.35040) Full Text: DOI
Farwig, Reinhard; Galdi, Giovanni P.; Sohr, Hermann A new class of weak solutions of the Navier-Stokes equations with nonhomogeneous data. (English) Zbl 1104.35032 J. Math. Fluid Mech. 8, No. 3, 423-444 (2006). MSC: 35Q30 76D05 35J25 35J65 35K60 PDFBibTeX XMLCite \textit{R. Farwig} et al., J. Math. Fluid Mech. 8, No. 3, 423--444 (2006; Zbl 1104.35032) Full Text: DOI
Farwig, R.; Galdi, G. P.; Sohr, H. Very weak solutions and large uniqueness classes of stationary Navier-Stokes equations in bounded domains of \(\mathbb R^2\). (English) Zbl 1119.35045 J. Differ. Equations 227, No. 2, 564-580 (2006). Reviewer: Etienne Emmrich (Berlin) MSC: 35Q30 76D03 76D05 35J55 76D07 35D05 PDFBibTeX XMLCite \textit{R. Farwig} et al., J. Differ. Equations 227, No. 2, 564--580 (2006; Zbl 1119.35045) Full Text: DOI
Farwig, Reinhard An \(L^q\)-analysis of viscous fluid flow past a rotating obstacle. (English) Zbl 1136.76340 Tohoku Math. J. (2) 58, No. 1, 129-147 (2006). MSC: 76D05 35C15 35Q35 76D99 76U05 PDFBibTeX XMLCite \textit{R. Farwig}, Tôhoku Math. J. (2) 58, No. 1, 129--147 (2006; Zbl 1136.76340) Full Text: DOI
Farwig, Reinhard Flow around rotating obstacles – analysis of a singular integral operator. (English) Zbl 1274.35281 Dumortier, Freddy (ed.) et al., EQUADIFF 2003. Proceedings of the international conference on differential equations, Hasselt, Belgium, July 22–26, 2003. Hackensack, NJ: World Scientific (ISBN 981-256-169-2/hbk). 371-376 (2005). MSC: 35Q35 45G10 47G30 76D05 PDFBibTeX XMLCite \textit{R. Farwig}, in: EQUADIFF 2003. Proceedings of the international conference on differential equations, Hasselt, Belgium, July 22--26, 2003. Hackensack, NJ: World Scientific. 371--376 (2005; Zbl 1274.35281)
Farwig, Reinhard Estimates of lower order derivatives of viscous fluid flow past a rotating obstacle. (English) Zbl 1101.35348 Mucha, Piotr (ed.) et al., Regularity and other aspects of the Navier-Stokes equations. Based on the conference on regularity and other qualitative aspects of the Navier-Stokes equations, Bȩdlewo, Poland, August 31–September 6, 2003. Warsaw: Polish Academy of Sciences, Institute of Mathematics. Banach Center Publications 70, 73-84 (2005). MSC: 35Q30 76D05 35C15 76U05 PDFBibTeX XMLCite \textit{R. Farwig}, Banach Cent. Publ. 70, 73--84 (2005; Zbl 1101.35348)
Farwig, Reinhard; Kozono, Hideo; Sohr, Hermann An \(L^q\)-approach to Stokes and Navier-Stokes equations in general domains. (English) Zbl 1111.35033 Acta Math. 195, No. 1, 21-53 (2005). Reviewer: Oleg Dementiev (Chelyabinsk) MSC: 35Q30 76D07 76D05 PDFBibTeX XMLCite \textit{R. Farwig} et al., Acta Math. 195, No. 1, 21--53 (2005; Zbl 1111.35033) Full Text: DOI
Farwig, Reinhard; Galdi, Giovanni P.; Sohr, Hermann Very weak solutions of stationary and instationary Navier-Stokes equations with nonhomogeneous data. (English) Zbl 1246.35148 Chipot, Michel (ed.) et al., Nonlinear elliptic and parabolic problems. A special tribute to the work of Herbert Amann, Zürich, Switzerland, June 28–30, 2004. Basel: Birkhäuser (ISBN 3-7643-7266-4/hbk). Progress in Nonlinear Differential Equations and their Applications 64, 113-136 (2005). Reviewer: Milan Pokorný (Praha) MSC: 35Q30 76D05 35J25 35J65 35K60 PDFBibTeX XMLCite \textit{R. Farwig} et al., Prog. Nonlinear Differ. Equ. Appl. 64, 113--136 (2005; Zbl 1246.35148) Full Text: DOI
Farwig, Reinhard; Hishida, Toshiaki; Müller, Detlef \(L^q\)-theory of a singular ”winding” integral operator arising from fluid dynamics. (English) Zbl 1057.35028 Pac. J. Math. 215, No. 2, 297-312 (2004). Reviewer: Uwe Kähler (Aveiro) MSC: 35Q30 76U05 35B45 47G10 76D05 42B25 PDFBibTeX XMLCite \textit{R. Farwig} et al., Pac. J. Math. 215, No. 2, 297--312 (2004; Zbl 1057.35028) Full Text: DOI
Farwig, Reinhard Weighted \(L^q\)-Helmholtz decompositions in infinite cylinders and in infinite layers. (English) Zbl 1038.35068 Adv. Differ. Equ. 8, No. 3, 357-384 (2003). Reviewer: Titus Petrila (Cluj-Napoca) MSC: 35Q35 35J20 35J25 76D05 PDFBibTeX XMLCite \textit{R. Farwig}, Adv. Differ. Equ. 8, No. 3, 357--384 (2003; Zbl 1038.35068)
Farwig, Reinhard; Sohr, Hermann Weighted estimates for the Oseen equations and the Navier-Stokes equations in exterior domains. (English) Zbl 0934.35120 Heywood, J. G. (ed.) et al., Theory of the Navier-Stokes equations. Proceedings of the third international conference on the Navier-Stokes equations: theory and numerical methods, Oberwolfach, Germany, June 5-11, 1994. Singapore: World Scientific. Ser. Adv. Math. Appl. Sci. 47, 11-30 (1998). Reviewer: Georg V.Jaiani (Tbilisi) MSC: 35Q30 76D05 35B40 PDFBibTeX XMLCite \textit{R. Farwig} and \textit{H. Sohr}, Ser. Adv. Math. Appl. Sci. 47, 11--30 (1998; Zbl 0934.35120)
Farwig, R.; Sohr, H. Global estimates in weighted spaces of weak solutions of the Navier-Stokes equations in exterior domains. (English) Zbl 0855.35099 Arch. Math. 67, No. 4, 319-330 (1996). Reviewer: R.Farwig (Darmstadt) MSC: 35Q30 76D05 76D07 PDFBibTeX XMLCite \textit{R. Farwig} and \textit{H. Sohr}, Arch. Math. 67, No. 4, 319--330 (1996; Zbl 0855.35099) Full Text: DOI
Farwig, Reinhard; Sohr, Hermann Weighted energy inequalities for the Navier-Stokes equations in exterior domains. (English) Zbl 0833.35107 Appl. Anal. 58, No. 1-2, 157-173 (1995). Reviewer: R.Farwig (Darmstadt) MSC: 35Q30 76D05 PDFBibTeX XMLCite \textit{R. Farwig} and \textit{H. Sohr}, Appl. Anal. 58, No. 1--2, 157--173 (1995; Zbl 0833.35107) Full Text: DOI
Farwig, Reinhard; Sohr, Hermann On the Stokes and Navier-Stokes system for domains with noncompact boundary in \(L^ q\)-spaces. (English) Zbl 0836.35117 Math. Nachr. 170, 53-77 (1994). Reviewer: Y.R.Romanovsky (Pereslavl’-Zalesskij) MSC: 35Q30 76D05 35D05 PDFBibTeX XMLCite \textit{R. Farwig} and \textit{H. Sohr}, Math. Nachr. 170, 53--77 (1994; Zbl 0836.35117) Full Text: DOI
Farwig, Reinhard; Sohr, Hermann The stationary and non-stationary Stokes system in exterior domains with non-zero divergence and non-zero boundary values. (English) Zbl 0798.35125 Math. Methods Appl. Sci. 17, No. 4, 269-291 (1994). Reviewer: T.O.Shaposhnikova (Linköping) MSC: 35Q30 76D05 76D07 PDFBibTeX XMLCite \textit{R. Farwig} and \textit{H. Sohr}, Math. Methods Appl. Sci. 17, No. 4, 269--291 (1994; Zbl 0798.35125) Full Text: DOI