Bulíček, Miroslav; Málek, Josef Large data analysis for Kolmogorov’s two-equation model of turbulence. (English) Zbl 1448.76094 Nonlinear Anal., Real World Appl. 50, 104-143 (2019). MSC: 76F60 35Q35 35A01 35D30 PDF BibTeX XML Cite \textit{M. Bulíček} and \textit{J. Málek}, Nonlinear Anal., Real World Appl. 50, 104--143 (2019; Zbl 1448.76094) Full Text: DOI arXiv
Liu, Qiao Regularity of weak solutions and the number of singular points to the 3D simplified nematic liquid crystal system. (English) Zbl 1423.76042 J. Funct. Anal. 277, No. 12, Article ID 108294, 33 p. (2019). MSC: 76A15 35B65 35Q35 PDF BibTeX XML Cite \textit{Q. Liu}, J. Funct. Anal. 277, No. 12, Article ID 108294, 33 p. (2019; Zbl 1423.76042) Full Text: DOI
Ożański, Wojciech S. The partial regularity theory of Caffarelli, Kohn, and Nirenberg and its sharpness. (English) Zbl 1441.35004 Advances in Mathematical Fluid Mechanics. Lecture Notes in Mathematical Fluid Mechanics. Cham: Birkhäuser (ISBN 978-3-030-26660-8/pbk; 978-3-030-26661-5/ebook). vi, 138 p. (2019). Reviewer: Florin Catrina (New York) MSC: 35-02 35B65 35Q30 76D03 76D05 PDF BibTeX XML Cite \textit{W. S. Ożański}, The partial regularity theory of Caffarelli, Kohn, and Nirenberg and its sharpness. Cham: Birkhäuser (2019; Zbl 1441.35004) Full Text: DOI
Chen, Fei; Guo, Boling The suitable weak solution for the Cauchy problem of the double-diffusive convection system. (English) Zbl 1417.35114 Appl. Anal. 98, No. 9, 1724-1740 (2019). MSC: 35Q35 35D30 76D03 35B65 PDF BibTeX XML Cite \textit{F. Chen} and \textit{B. Guo}, Appl. Anal. 98, No. 9, 1724--1740 (2019; Zbl 1417.35114) Full Text: DOI
Liu, Xian-Gao; Min, Jianzhong; Zhang, Xiaotao \(L^{3,\infty}\) solutions of the liquid crystals system. (English) Zbl 1426.76045 J. Differ. Equations 267, No. 4, 2643-2670 (2019). Reviewer: Alain Brillard (Riedisheim) MSC: 76A15 35Q35 PDF BibTeX XML Cite \textit{X.-G. Liu} et al., J. Differ. Equations 267, No. 4, 2643--2670 (2019; Zbl 1426.76045) Full Text: DOI
Ożański, Wojciech S.; Robinson, James C. Partial regularity for a surface growth model. (English) Zbl 1408.35065 SIAM J. Math. Anal. 51, No. 1, 228-255 (2019). Reviewer: Alain Brillard (Riedisheim) MSC: 35K25 35K55 76D03 74K35 35Q35 35Q30 PDF BibTeX XML Cite \textit{W. S. Ożański} and \textit{J. C. Robinson}, SIAM J. Math. Anal. 51, No. 1, 228--255 (2019; Zbl 1408.35065) Full Text: DOI
Chen, Ya-zhou; He, Qiao-lin; Shi, Xiao-ding; Wang, Teng; Wang, Xiao-ping On the motion of shear-thinning heat-conducting incompressible fluid-rigid system. (English) Zbl 1403.35202 Acta Math. Appl. Sin., Engl. Ser. 34, No. 3, 534-552 (2018). MSC: 35Q30 35M10 76U05 35D30 76A05 35A01 PDF BibTeX XML Cite \textit{Y.-z. Chen} et al., Acta Math. Appl. Sin., Engl. Ser. 34, No. 3, 534--552 (2018; Zbl 1403.35202) Full Text: DOI
Ren, Wei; Wang, Yanqing; Wu, Gang Remarks on the singular set of suitable weak solutions for the three-dimensional Navier-Stokes equations. (English) Zbl 1401.35244 J. Math. Anal. Appl. 467, No. 2, 807-824 (2018). Reviewer: Eugene Postnikov (Kursk) MSC: 35Q30 35D30 76D05 PDF BibTeX XML Cite \textit{W. Ren} et al., J. Math. Anal. Appl. 467, No. 2, 807--824 (2018; Zbl 1401.35244) Full Text: DOI
Wang, Wendong; Zhang, Liqun; Zhang, Zhifei On the interior regularity criteria of the 3-D Navier-Stokes equations involving two velocity components. (English) Zbl 1397.35184 Discrete Contin. Dyn. Syst. 38, No. 5, 2609-2627 (2018). MSC: 35Q30 35B65 76D05 35B44 35D30 PDF BibTeX XML Cite \textit{W. Wang} et al., Discrete Contin. Dyn. Syst. 38, No. 5, 2609--2627 (2018; Zbl 1397.35184) Full Text: DOI arXiv
Berselli, Luigi C.; Spirito, Stefano On the construction of suitable weak solutions to the 3D Navier-Stokes equations in a bounded domain by an artificial compressibility method. (English) Zbl 1386.35321 Commun. Contemp. Math. 20, No. 1, Article ID 1650064, 16 p. (2018). MSC: 35Q30 35A35 76M20 PDF BibTeX XML Cite \textit{L. C. Berselli} and \textit{S. Spirito}, Commun. Contemp. Math. 20, No. 1, Article ID 1650064, 16 p. (2018; Zbl 1386.35321) Full Text: DOI arXiv
Kim, Jaemyoung Local regularity criteria of a suitable weak solution to MHD equations. (English) Zbl 1399.35111 Acta Math. Sci., Ser. B, Engl. Ed. 37, No. 4, 1033-1047 (2017). MSC: 35B65 35D30 35Q35 76W05 PDF BibTeX XML Cite \textit{J. Kim}, Acta Math. Sci., Ser. B, Engl. Ed. 37, No. 4, 1033--1047 (2017; Zbl 1399.35111) Full Text: DOI
Kim, Jae-Myoung Interior condition on suitable weak solutions to the 3D MHD equations via pressure. (English) Zbl 1384.35091 Acta Appl. Math. 152, No. 1, 83-91 (2017). MSC: 35Q35 76W05 35B65 35D30 PDF BibTeX XML Cite \textit{J.-M. Kim}, Acta Appl. Math. 152, No. 1, 83--91 (2017; Zbl 1384.35091) Full Text: DOI
Li, Yuan The Minkowski dimension of interior singular points of suitable weak solutions of the three dimensional of incompressible Boussinesq equations. (Chinese. English summary) Zbl 1389.35259 J. Hubei Univ., Nat. Sci. 39, No. 3, 241-247 (2017). MSC: 35Q35 35B65 35D30 PDF BibTeX XML Cite \textit{Y. Li}, J. Hubei Univ., Nat. Sci. 39, No. 3, 241--247 (2017; Zbl 1389.35259) Full Text: DOI
Choe, Hi Jun; Jang, Yunsoo; Yang, Minsuk Existence of suitable weak solutions to the Navier-Stokes equations in time varying domains. (English) Zbl 1386.35145 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 163, 163-176 (2017). MSC: 35K20 35A01 35D30 PDF BibTeX XML Cite \textit{H. J. Choe} et al., Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 163, 163--176 (2017; Zbl 1386.35145) Full Text: DOI
Fang, Daoyuan; Liu, Chun; Qian, Chenyin On partial regularity problem for 3D Boussinesq equations. (English) Zbl 1372.35233 J. Differ. Equations 263, No. 7, 4156-4221 (2017). MSC: 35Q35 76B03 76D03 35B65 35D30 PDF BibTeX XML Cite \textit{D. Fang} et al., J. Differ. Equations 263, No. 7, 4156--4221 (2017; Zbl 1372.35233) Full Text: DOI
Ma, Wenya; Feng, Jiqiang Interior regularity criterion for incompressible Ericksen-Leslie system. (English) Zbl 1360.35185 Bound. Value Probl. 2017, Paper No. 62, 7 p. (2017). MSC: 35Q35 76D03 PDF BibTeX XML Cite \textit{W. Ma} and \textit{J. Feng}, Bound. Value Probl. 2017, Paper No. 62, 7 p. (2017; Zbl 1360.35185) Full Text: DOI
Luo, Wei; Yin, Zhaoyang The Liouville theorem and the \(L^{2}\) decay for the FENE dumbbell model of polymeric flows. (English) Zbl 1366.35134 Arch. Ration. Mech. Anal. 224, No. 1, 209-231 (2017). Reviewer: Alain Brillard (Riedisheim) MSC: 35Q35 35B53 35Q84 82C31 76D05 35D30 35D35 PDF BibTeX XML Cite \textit{W. Luo} and \textit{Z. Yin}, Arch. Ration. Mech. Anal. 224, No. 1, 209--231 (2017; Zbl 1366.35134) Full Text: DOI
Chae, Dongho; Lee, Jihoon On the geometric regularity conditions for the 3D Navier-Stokes equations. (English) Zbl 1358.35089 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 151, 265-273 (2017). MSC: 35Q30 76D03 76D05 35B65 35D30 35B44 PDF BibTeX XML Cite \textit{D. Chae} and \textit{J. Lee}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 151, 265--273 (2017; Zbl 1358.35089) Full Text: DOI arXiv
Berselli, Luigi C.; Spirito, Stefano Suitable weak solutions to the 3D Navier-Stokes equations are constructed with the Voigt approximation. (English) Zbl 1371.35191 J. Differ. Equations 262, No. 5, 3285-3316 (2017). Reviewer: Ruxandra Stavre (Bucureşti) MSC: 35Q30 35A35 35D30 35B65 35B45 76D05 PDF BibTeX XML Cite \textit{L. C. Berselli} and \textit{S. Spirito}, J. Differ. Equations 262, No. 5, 3285--3316 (2017; Zbl 1371.35191) Full Text: DOI arXiv
Chen, Yukang; Wei, Changhua Partial regularity of solutions to the fractional Navier-Stokes equations. (English) Zbl 1426.76087 Discrete Contin. Dyn. Syst. 36, No. 10, 5309-5322 (2016). MSC: 76D03 35Q30 PDF BibTeX XML Cite \textit{Y. Chen} and \textit{C. Wei}, Discrete Contin. Dyn. Syst. 36, No. 10, 5309--5322 (2016; Zbl 1426.76087) Full Text: DOI
Bae, Hyeong-Ohk; Kang, Kyungkeun; Kim, Myeonghyeon Local regularity criteria of the Navier-Stokes equations with slip boundary conditions. (English) Zbl 1341.35097 J. Korean Math. Soc. 53, No. 3, 597-621 (2016). MSC: 35Q30 35D30 76D05 35B65 PDF BibTeX XML Cite \textit{H.-O. Bae} et al., J. Korean Math. Soc. 53, No. 3, 597--621 (2016; Zbl 1341.35097) Full Text: DOI Link
Tan, Wenke; Yin, Zhaoyang On the number of singular points to the flow of nematic liquid crystals. (English) Zbl 1334.35255 J. Evol. Equ. 16, No. 1, 233-240 (2016). MSC: 35Q35 76A15 PDF BibTeX XML Cite \textit{W. Tan} and \textit{Z. Yin}, J. Evol. Equ. 16, No. 1, 233--240 (2016; Zbl 1334.35255) Full Text: DOI
Wolf, Jörg On the local regularity of suitable weak solutions to the generalized Navier-Stokes equations. (English) Zbl 1323.35135 Ann. Univ. Ferrara, Sez. VII, Sci. Mat. 61, No. 1, 149-171 (2015). Reviewer: Gheorghe Moroşanu (Budapest) MSC: 35Q30 76D05 35B65 76N10 76A05 PDF BibTeX XML Cite \textit{J. Wolf}, Ann. Univ. Ferrara, Sez. VII, Sci. Mat. 61, No. 1, 149--171 (2015; Zbl 1323.35135) Full Text: DOI
Neustupa, Jiří A geometric improvement of the velocity-pressure local regularity criterion for a suitable weak solution to the Navier-Stokes equations. (English) Zbl 1349.35276 Math. Bohem. 139, No. 4, 685-698 (2014). MSC: 35Q30 35B65 35D30 76D05 PDF BibTeX XML Cite \textit{J. Neustupa}, Math. Bohem. 139, No. 4, 685--698 (2014; Zbl 1349.35276) Full Text: Link
Neustupa, Jiří A note on local interior regularity of a suitable weak solution to the Navier-Stokes problem. (English) Zbl 1260.35125 Discrete Contin. Dyn. Syst., Ser. S 6, No. 5, 1391-1400 (2013). MSC: 35Q30 76D03 76D05 PDF BibTeX XML Cite \textit{J. Neustupa}, Discrete Contin. Dyn. Syst., Ser. S 6, No. 5, 1391--1400 (2013; Zbl 1260.35125) Full Text: DOI
Feireisl, Eduard; Jin, Bum Ja; Novotný, Antonín Relative entropies, suitable weak solutions, and weak-strong uniqueness for the compressible Navier-Stokes system. (English) Zbl 1256.35054 J. Math. Fluid Mech. 14, No. 4, 717-730 (2012). MSC: 35Q30 35D30 76N10 PDF BibTeX XML Cite \textit{E. Feireisl} et al., J. Math. Fluid Mech. 14, No. 4, 717--730 (2012; Zbl 1256.35054) Full Text: DOI arXiv
Han, Pigong; He, Cheng Partial regularity of suitable weak solutions to the four-dimensional incompressible magneto-hydrodynamic equations. (English) Zbl 1256.35081 Math. Methods Appl. Sci. 35, No. 11, 1335-1355 (2012). MSC: 35Q35 35D30 35B65 PDF BibTeX XML Cite \textit{P. Han} and \textit{C. He}, Math. Methods Appl. Sci. 35, No. 11, 1335--1355 (2012; Zbl 1256.35081) Full Text: DOI
Bulíček, M.; Lewandowski, R.; Málek, J. On evolutionary Navier-Stokes-Fourier type systems in three spatial dimensions. (English) Zbl 1240.35378 Commentat. Math. Univ. Carol. 52, No. 1, 89-114 (2011). MSC: 35Q30 35Q35 76F60 PDF BibTeX XML Cite \textit{M. Bulíček} et al., Commentat. Math. Univ. Carol. 52, No. 1, 89--114 (2011; Zbl 1240.35378) Full Text: EMIS EuDML
Bulíček, M.; Ulrych, O. Planar flows of incompressible heat-conducting shear-thinning fluids - existence analysis. (English) Zbl 1224.35312 Appl. Math., Praha 56, No. 1, 7-38 (2011). MSC: 35Q30 35D30 76D03 76A05 PDF BibTeX XML Cite \textit{M. Bulíček} and \textit{O. Ulrych}, Appl. Math., Praha 56, No. 1, 7--38 (2011; Zbl 1224.35312) Full Text: DOI EuDML
Donatelli, Donatella; Spirito, Stefano Weak solutions of Navier-Stokes equations constructed by artificial compressibility method are suitable. (English) Zbl 1217.35134 J. Hyperbolic Differ. Equ. 8, No. 1, 101-113 (2011). MSC: 35Q30 76Q05 76N10 35A35 76D05 76D03 PDF BibTeX XML Cite \textit{D. Donatelli} and \textit{S. Spirito}, J. Hyperbolic Differ. Equ. 8, No. 1, 101--113 (2011; Zbl 1217.35134) Full Text: DOI arXiv
Röckner, Michael; Zhang, Xicheng Tamed 3D Navier – Stokes equation: existence, uniqueness and regularity. (English) Zbl 1180.35417 Infin. Dimens. Anal. Quantum Probab. Relat. Top. 12, No. 4, 525-549 (2009). MSC: 35Q30 76D05 76D03 PDF BibTeX XML Cite \textit{M. Röckner} and \textit{X. Zhang}, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 12, No. 4, 525--549 (2009; Zbl 1180.35417) Full Text: DOI arXiv
Chou, Kai-Seng; Du, Shi-Zhong Estimates on the Hausdorff dimension of the rupture set of a thin film. (English) Zbl 1157.35454 SIAM J. Math. Anal. 40, No. 2, 790-823 (2008). MSC: 35Q35 76A20 35B35 93D20 PDF BibTeX XML Cite \textit{K.-S. Chou} and \textit{S.-Z. Du}, SIAM J. Math. Anal. 40, No. 2, 790--823 (2008; Zbl 1157.35454) Full Text: DOI
Chen, Chiun-Chuan; Strain, Robert M.; Yau, Horng-Tzer; Tsai, Tai-Peng Lower bound on the blow-up rate of the axisymmetric Navier-Stokes equations. (English) Zbl 1154.35068 Int. Math. Res. Not. 2008, Article ID rnn016, 31 p. (2008). Reviewer: Pavel Burda (Praha) MSC: 35Q30 35B05 76D05 76D03 35B65 35D10 PDF BibTeX XML Cite \textit{C.-C. Chen} et al., Int. Math. Res. Not. 2008, Article ID rnn016, 31 p. (2008; Zbl 1154.35068) Full Text: DOI arXiv
Biryuk, Andrei; Craig, Walter; Ibrahim, Slim Construction of suitable weak solutions of the Navier-Stokes equations. (English) Zbl 1205.35187 Chen, Gui-Qiang (ed.) et al., Stochastic analysis and partial differential equations. Emphasis year 2004–2005 on stochastic analysis and partial differential equations, Evanston, IL, USA. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4059-7/pbk). Contemporary Mathematics 429, 1-18 (2007). Reviewer: Ruxandra Stavre (Bucureşti) MSC: 35Q30 76D03 35D30 PDF BibTeX XML Cite \textit{A. Biryuk} et al., Contemp. Math. 429, 1--18 (2007; Zbl 1205.35187)
Gustafson, Stephen; Kang, Kyungkeun; Tsai, Tai-Peng Regularity criteria for suitable weak solutions of the Navier-Stokes equations near the boundary. (English) Zbl 1159.35396 J. Differ. Equations 226, No. 2, 594-618 (2006). MSC: 35Q30 35B65 35D10 76D03 76D05 PDF BibTeX XML Cite \textit{S. Gustafson} et al., J. Differ. Equations 226, No. 2, 594--618 (2006; Zbl 1159.35396) Full Text: DOI arXiv
Neustupa, Jiří; Penel, Patrick Regularity of a weak solution to the Navier-Stokes equation in dependence on eigenvalues and eigenvectors of the rate of deformation tensor. (English) Zbl 1078.35088 Rodrigues, José F. (ed.) et al., Trends in partial differential equations of mathematical physics. Selected papers of the international conference held on the occasion of the 70th birthday of V. A. Solonnikov, Óbidos, Portugal, June 7–10, 2003. Basel: Birkhäuser (ISBN 3-7643-7165-X/hbk). Progress in Nonlinear Differential Equations and their Applications 61, 197-212 (2005). Reviewer: Milan Pokorný (Praha) MSC: 35Q30 76D03 35D10 PDF BibTeX XML Cite \textit{J. Neustupa} and \textit{P. Penel}, Prog. Nonlinear Differ. Equ. Appl. 61, 197--212 (2005; Zbl 1078.35088)
Skalák, Zdeněk; Kučera, Petr A note on coupling of velocity components in the Navier-Stokes equations. (English) Zbl 1042.35052 ZAMM, Z. Angew. Math. Mech. 84, No. 2, 124-127 (2004). MSC: 35Q30 76D03 PDF BibTeX XML Cite \textit{Z. Skalák} and \textit{P. Kučera}, ZAMM, Z. Angew. Math. Mech. 84, No. 2, 124--127 (2004; Zbl 1042.35052) Full Text: DOI
Kučera, Petr; Skalák, Zdeněk A note on the generalized energy inequality in the Navier-Stokes equations. (English) Zbl 1099.35099 Appl. Math., Praha 48, No. 6, 537-545 (2003). Reviewer: Milan Pokorný (Praha) MSC: 35Q35 35Q30 76D05 PDF BibTeX XML Cite \textit{P. Kučera} and \textit{Z. Skalák}, Appl. Math., Praha 48, No. 6, 537--545 (2003; Zbl 1099.35099) Full Text: DOI EuDML
Seregin, G. A. Remarks on the regularity of weak solutions to the Navier-Stokes equations near the boundary. (English. Russian original) Zbl 1083.35098 J. Math. Sci., New York 127, No. 2, 1915-1922 (2005); translation from Zap. Nauchn. Semin. POMI 295, 168-179 (2003). Reviewer: Il’ya Sh. Mogilevskij (Tver’) MSC: 35Q30 35D10 76D03 76D05 PDF BibTeX XML Cite \textit{G. A. Seregin}, J. Math. Sci., New York 127, No. 2, 1915--1922 (2003; Zbl 1083.35098); translation from Zap. Nauchn. Semin. POMI 295, 168--179 (2003) Full Text: DOI
Skalák, Zdeněk Conditions of Prodi-Serrin’s type for local regularity of suitable weak solutions to the Navier-Stokes equations. (English) Zbl 1090.35148 Commentat. Math. Univ. Carol. 43, No. 4, 619-639 (2002). Reviewer: Milan Pokorný (Praha) MSC: 35Q35 35B65 76D05 PDF BibTeX XML Cite \textit{Z. Skalák}, Commentat. Math. Univ. Carol. 43, No. 4, 619--639 (2002; Zbl 1090.35148) Full Text: EMIS EuDML
Nečas, Jindřich; Neustupa, Jiří New conditions for local regularity of a suitable weak solution to the Navier-Stokes equation. (English) Zbl 1010.35081 J. Math. Fluid Mech. 4, No. 3, 237-256 (2002). MSC: 35Q30 76D03 35B65 PDF BibTeX XML Cite \textit{J. Nečas} and \textit{J. Neustupa}, J. Math. Fluid Mech. 4, No. 3, 237--256 (2002; Zbl 1010.35081) Full Text: DOI
Seregin, G. A. Local regularity of suitable weak solutions to the Navier-Stokes equations near the boundary. (English) Zbl 0997.35044 J. Math. Fluid Mech. 4, No. 1, 1-29 (2002). Reviewer: Il’ya Sh. Mogilevskii (Tver’) MSC: 35Q30 76D03 35D30 PDF BibTeX XML Cite \textit{G. A. Seregin}, J. Math. Fluid Mech. 4, No. 1, 1--29 (2002; Zbl 0997.35044) Full Text: DOI
Seregin, G. A. On the number of singular points of weak solutions to the Navier-Stokes equations. (English) Zbl 1030.35133 Commun. Pure Appl. Math. 54, No. 8, 1019-1028 (2001). Reviewer: Vasile Ionescu (Bucureşti) MSC: 35Q30 35A20 76D03 76D05 35D99 PDF BibTeX XML Cite \textit{G. A. Seregin}, Commun. Pure Appl. Math. 54, No. 8, 1019--1028 (2001; Zbl 1030.35133) Full Text: DOI
Choe, Hi Jun; Lewis, John L. On the singular set in the Navier-Stokes equations. (English) Zbl 0965.35115 J. Funct. Anal. 175, No. 2, 348-369 (2000). Reviewer: Milan Pokorný (Columbia) MSC: 35Q30 76D03 PDF BibTeX XML Cite \textit{H. J. Choe} and \textit{J. L. Lewis}, J. Funct. Anal. 175, No. 2, 348--369 (2000; Zbl 0965.35115) Full Text: DOI