| 1 | Serrin J . On the interior regularity of weak solutions of the Navier-Stokes equations. Arch Ration Mech Anal, 1962, 9, 187- 195 | | 2 | Bae H , Choe H . A regularity criterion for the Navier-Stokes equations. Comm Partial Differential Equations, 2007, 32, 1173- 1187 | | 3 | Bae H , Wolf J . A local regularity condition involving two velocity components of Serrin-type for the Navier-Stokes equations. C R Math Acad Sci Paris, 2016, 354, 167- 174 | | 4 | Beirao da Veiga H . A new regularity class for the Navier-Stokes equations in $ {\mathbb R}.{n} $. Chinese Annals of Mathematics Series B, 1995, 16, 407- 412 | | 5 | Berselli L , Manfrin R . On a theorem by Sohr for the Navier-Stokes equations. J Evol Equa, 2004, 4, 193- 211 | | 6 | Bosia S , Pata V , Robinson J . A weak-$ L.p $ Prodi-Serrint type regularity criterion for the Navier-Stokes equations. J Math Fluid Mech, 2014, 16, 721- 725 | | 7 | Chae D , Choe H . Regularity of solutions to the Navier-Stokes equation. Electron J Differential Equations, 1999, 5, 1- 7 | | 8 | Chen Q , Zhang Z . Regularity criterion via two components of vorticity on weak solutions to the Navier-Stokes equations in $ {\mathbb R}.{3} $. J Differential Equations, 2005, 216, 470- 481 | | 9 | Chen Z , Price W . Blow-up rate estimates for weak solutions of the Navier-Stokes equations. R Soc Lond Proc Ser A Math Phys Eng Sci, 2001, 457, 2625- 2642 | | 10 | Dong B , Chen Z . Regularity criterion of weak solutions to the 3D Navier-Stokes equations via two velocity components. J Math Anal Appl, 2008, 338, 1- 10 | | 11 | Ji X , Wang Y , Wei W . New regularity criteria based on pressure or gradient of velocity in Lorentz spaces for the 3D Navier-Stokes equations. J Math Fluid Mech, 2020, 22 (1): Artcile 13 | | 12 | Jia X , Zhou Y . Ladyzhenskaya-Prodi-Serrin type regularity criteria for the 3D incompressible MHD equations in terms of $ 3\times3 $ mixture matrices. Nonlinearity, 2015, 28, 3289- 3307 | | 13 | Kim H , Kozono H . Interior regularity criteria in weak spaces for the Navier-Stokes equations. Manuscripta Math, 2004, 115, 85- 100 | | 14 | Takahashi S . On interior regularity criteria for weak solutions of the Navier-Stokes equations. Manuscripta Math, 1990, 69, 237- 254 | | 15 | Wang W , Zhang Z . On the interior regularity criteria and the number of singular points to the Navier-Stokes equations. J Anal Math, 2014, 123, 139- 170 | | 16 | Wang W , Zhang L , Zhang Z . On the interior regularity criteria of the 3-D Navier-Stokes equations involving two velocity components. Discrete Contin Dyn Syst, 2018, 38, 2609- 2627 | | 17 | Wang Y, Wei W, Yu H. $ \varepsilon $-regularity criteria in Lorentz spaces to the 3D Navier-Stokes equations. 2019, arXiv: 1909.09957 | | 18 | Wang Y , Wu G , Zhou D . Some interior regularity criteria involving two components for weak solutions to the 3D Navier-Stokes equations. J Math Fluid Mech, 2018, 20, 2147- 2159 | | 19 | L?fstr?m J . Interpolation Spaces. Berlin: Springer-Verlag, 1976 | | 20 | Grafakos L . Classical Fourier Analysis. New York: Springer, 2014 | | 21 | Leray J . Sur le mouvement déun liquide visqueux emplissant léspace. Acta Math, 1934, 63, 193- 248 | | 22 | Malý J. Advanced theory of differentiation-Lorentz spaces. 2003. http://www.karlin.mff.cuni.cz/~maly/lorentz.pdf | | 23 | He C , Wang Y . On the regularity criteria for weak solutions to the magnetohydrodynamic equations. J Differential Equations, 2007, 238, 1- 17 | | 24 | Sohr H . A regularity class for the Navier-Stokes equations in Lorentz spaces. J Evol Equa, 2001, 1, 441- 467 | | 25 | He C , Wang Y . Limiting case for the regularity criterion of the Navier-Stokes equations and the magnetohydrodynamic equations. Sci China Math, 2010, 53, 1767- 1774 | | 26 | O'Neil R . Convolution operators and $ L.{p, q} $ spaces. Duke Math J, 1963, 30, 129- 142 | | 27 | Tartar L . Imbedding theorems of Sobolev spaces into Lorentz spaces. Boll Unione Mat Ital Sez B Artic Ric Mat, 1998, 1, 479- 500 | | 28 | Carrillo J , Ferreira L . Self-similar solutions and large time asymptotics for the dissipative quasi-geostrophic equation. Monatsh Math, 2007, 151, 111- 142 |
|
)