Institute of Mathematics

References:
[1] H. Beirão da Veiga: A new regularity class for the Navier-Stokes equations in $\mathbb R^n$. Chin. Ann. Math., Ser. B 16 (1995), 407-412. MR 1380578 | Zbl 0837.35111
[2] C. Cao: Sufficient conditions for the regularity to the 3D Navier-Stokes equations. Discrete Contin. Dyn. Syst. 26 (2010), 1141-1151. DOI 10.3934/dcds.2010.26.1141 | MR 2600739 | Zbl 1186.35136
[3] C. Cao, E. S. Titi: Regularity criteria for the three-dimensional Navier-Stokes equations. Indiana Univ. Math. J. 57 (2008), 2643-2661. DOI 10.1512/iumj.2008.57.3719 | MR 2482994 | Zbl 1159.35053
[4] J.-Y. Chemin, P. Zhang: On the critical one component regularity for 3-D Navier-Stokes systems. Ann. Sci. Éc. Norm. Supér. (4) 49 (2016), 131-167. DOI 10.24033/asens.2278 | MR 3465978 | Zbl 1342.35210
[5] J.-Y. Chemin, P. Zhang, Z. Zhang: On the critical one component regularity for 3-D Navier-Stokes system: general case. Arch. Ration. Mech. Anal. 224 (2017), 871-905. DOI 10.1007/s00205-017-1089-0 | MR 3621812 | Zbl 1371.35193
[6] L. Escauriaza, G. A. Serëgin, V. Šverák: $L_{3,\infty}$-solutions of Navier-Stokes equations and backward uniqueness. Russ. Math. Surv. 58 (2003), 211-250; translation from Usp. Mat. Nauk 58 (2003), 3-44. DOI 10.1070/RM2003v058n02ABEH000609 | MR 1992563 | Zbl 1064.35134
[7] Z. Guo, M. Caggio, Z. Skalák: Regularity criteria for the Navier-Stokes equations based on one component of velocity. Nonlinear Anal., Real World Appl. 35 (2017), 379-396. DOI 10.1016/j.nonrwa.2016.11.005 | MR 3595332 | Zbl 1360.35146
[8] E. Hopf: Über die Anfangswertaufgabe für die hydrodynamischen Grundgleichungen. Math. Nachr. 4 (1951), 213-231. (In German.) DOI 10.1002/mana.3210040121 | MR 0050423 | Zbl 0042.10604
[9] X. Jia, Y. Zhou: Remarks on regularity criteria for the Navier-Stokes equations via one velocity component. Nonlinear Anal., Real World Appl. 15 (2014), 239-245. DOI 10.1016/j.nonrwa.2013.08.002 | MR 3110568 | Zbl 1297.35168
[10] I. Kukavica, M. Ziane: One component regularity for the Navier-Stokes equations. Nonlinearity 19 (2006), 453-469. DOI 10.1088/0951-7715/19/2/012 | MR 2199398 | Zbl 1149.35069
[11] I. Kukavica, M. Ziane: Navier-Stokes equations with regularity in one direction. J. Math. Phys. 48 (2007), Article ID 065203, 10 pages. DOI 10.1063/1.2395919 | MR 2337002 | Zbl 1144.81373
[12] J. Leray: Sur le mouvement d'un liquide visqueux emplissant l'espace. Acta Math. 63 (1934), 193-248. (In French.) DOI 10.1007/BF02547354 | MR 1555394 | JFM 60.0726.05
[13] J. Neustupa, A. Novotný, P. Penel: An interior regularity of a weak solution to the Navier-Stokes equations in dependence on one component of velocity. Topics in Mathematical Fluid Mechanics. Quad. Mat. 10, Aracne, Rome, 2002, pp. 163-183. MR 2051774 | Zbl 1050.35073
[14] P. Penel, M. Pokorný: Some new regularity criteria for the Navier-Stokes equations containing gradient of the velocity. Appl. Math., Praha 49 (2004), 483-493. DOI 10.1023/B:APOM.0000048124.64244.7e | MR 2086090 | Zbl 1099.35101
[15] P. Penel, M. Pokorný: On anisotropic regularity criteria for the solutions to 3D Navier-Stokes equations. J. Math. Fluid Mech. 13 (2011), 341-353. DOI 10.1007/s00021-010-0038-6 | MR 2824487 | Zbl 1270.35354
[16] M. Pokorný: On the result of He concerning the smoothness of solutions to the Navier-Stokes equations. Electron. J. Differ. Equ. 2003 (2003), Article No. 11, 8 pages. MR 1958046 | Zbl 1014.35073
[17] G. Prodi: Un teorema di unicità per le equazioni di Navier-Stokes. Ann. Mat. Pura Appl. (4) 48 (1959), 173-182. (In Italian.) DOI 10.1007/BF02410664 | MR 0126088 | Zbl 0148.08202
[18] J. C. Robinson, J. L. Rodrigo, W. Sadowski: The Three-Dimensional Navier-Stokes Equations. Classical Theory. Cambridge Studies in Advanced Mathematics 157, Cambridge University Press, Cambridge (2016). DOI 10.1017/CBO9781139095143 | MR 3616490 | Zbl 1358.35002
[19] J. Serrin: On the interior regularity of weak solutions of the Navier-Stokes equations. Arch. Ration. Mech. Anal. 9 (1962), 187-195. DOI 10.1007/BF00253344 | MR 0136885 | Zbl 0106.18302
[20] Z. Skalák: On the regularity of the solutions to the Navier-Stokes equations via the gradient of one velocity component. Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 104 (2014), 84-89. DOI 10.1016/j.na.2014.03.018 | MR 3196890 | Zbl 1291.35192
[21] R. Temam: Navier-Stokes Equations. Theory and Numerical Analysis. AMS Chelsea Publishing, Providence (2001). DOI 10.1090/chel/343 | MR 1846644 | Zbl 0981.35001
[22] Z. Zhang: An almost Serrin-type regularity criterion for the Navier-Stokes equations involving the gradient of one velocity component. Z. Angew. Math. Phys. 66 (2015), 1707-1715. DOI 10.1007/s00033-015-0500-7 | MR 3377710 | Zbl 1325.35147
[23] Z. Zhang: An improved regularity criterion for the Navier-Stokes equations in terms of one directional derivative of the velocity field. Bull. Math. Sci. 8 (2018), 33-47. DOI 10.1007/s13373-016-0098-x | MR 3775266 | Zbl 1393.35152
[24] Y. Zhou: A new regularity criterion for the Navier-Stokes equations in terms of the gradient of one velocity component. Methods Appl. Anal. 9 (2002), 563-578. DOI 10.4310/MAA.2002.v9.n4.a5 | MR 2006605 | Zbl 1166.35359
[25] Y. Zhou: A new regularity criterion for weak solutions to the Navier-Stokes equations. J. Math. Pures Appl. (9) 84 (2005), 1496-1514. DOI 10.1016/j.matpur.2005.07.003 | MR 2181458 | Zbl 1092.35081
[26] Y. Zhou, M. Pokorný: On a regularity criterion for the Navier-Stokes equations involving gradient of one velocity component. J. Math. Phys. 50 (2009), Article ID 123514, 11 pages. DOI 10.1063/1.3268589 | MR 2582610 | Zbl 1373.35226
[27] Y. Zhou, M. Pokorný: On the regularity of the solutions of the Navier-Stokes equations via one velocity component. Nonlinearity 23 (2010), 1097-1107. DOI 10.1088/0951-7715/23/5/004 | MR 2630092 | Zbl 1190.35179