Logarithmically improved regularity criteria for the Navier–Stokes equations in multiplier spaces

Abstract The aim of this paper is to establish some logarithmically improved regularity criteria in term of the multiplier spaces to the Navier–Stokes equations.

[1]  Yong Zhou,et al.  On a regularity criterion in terms of the gradient of pressure for the Navier-Stokes equations in $$\mathbb{R}^{N}$$ , 2006 .

[2]  J. Serrin.  The initial value problem for the Navier-Stokes equations , 1963 .

[3]  S. Gala.  THE BANACH SPACE OF LOCAL MEASURES AND REGULARITY CRITERION TO THE NAVIER-STOKES EQUATIONS , 2007 .

[4]  Michael Struwe,et al.  On partial regularity results for the navier‐stokes equations , 1988 .

[5]  Multipliers spaces, Muckenhoupt weights and pseudo-differential operators , 2006 .

[6]  Da Veiga,et al.  A new regularity class for the Navier-Stokes equations in R^n , 1995 .

[7]  G. Prodi.  Un teorema di unicità per le equazioni di Navier-Stokes , 1959 .

[8]  Alexis Vasseur,et al.  Log Improvement of the Prodi-Serrin Criteria for Navier-Stokes Equations , 2007, 0705.3659.

[9]  Yong Zhou,et al.  Regularity criteria for the solutions to the 3D MHD equations in the multiplier space , 2010 .

[10]  Hideo Kozono,et al.  Regularity criterion of weak solutions to the Navier-Stokes equations , 1997 .

[11]  Yong Zhou,et al.  Regularity criteria in terms of pressure for the 3-D Navier-Stokes equations in a generic domain , 2004 .

[12]  Jean Leray,et al.  Sur le mouvement d'un liquide visqueux emplissant l'espace , 1934 .

[13]  Yong Zhou,et al.  A new regularity criterion for weak solutions to the Navier–Stokes equations , 2005 .

[14]  E. Hopf,et al.  Über die Anfangswertaufgabe für die hydrodynamischen Grundgleichungen. Erhard Schmidt zu seinem 75. Geburtstag gewidmet , 1950 .

[15]  Tosio Kato,et al.  Remarks on the breakdown of smooth solutions for the 3-D Euler equations , 1984 .

[16]  Yong Zhou,et al.  A New Regularity Criterion for the Navier-Stokes Equations in Terms of the Direction of Vorticity , 2005 .

[17]  S. Gala.  REGULARITY CRITERION ON WEAK SOLUTIONS TO THE NAVIER-STOKES EQUATIONS , 2008 .

[18]  Stephen Montgomery-Smith.  Conditions Implying Regularity of the Three Dimensional Navier-Stokes Equation , 2003 .