Regularity criteria for the 3D density-dependent Boussinesq equations

We consider the 3D density-dependent Boussinesq equations and the classical Boussinesq equations with partial viscosity terms. We prove some regularity criteria of strong solutions for the Boussinesq equations.

[1]  Yoshikazu Giga,et al.  Solutions for semilinear parabolic equations in Lp and regularity of weak solutions of the Navier-Stokes system , 1986 .

[2]  Hyunseok Kim,et al.  A Blow-Up Criterion for the Nonhomogeneous Incompressible Navier-Stokes Equations , 2006, SIAM J. Math. Anal..

[3]  J. Serrin On the interior regularity of weak solutions of the Navier-Stokes equations , 1962 .

[4]  Wolf von Wahl,et al.  On the regularity of the pressure of weak solutions of Navier-Stokes equations , 1986 .

[5]  Tohru Ozawa,et al.  Interpolation inequalities in Besov spaces , 2002 .

[6]  P. Lions Mathematical topics in fluid mechanics , 1996 .

[7]  Takayoshi Ogawa,et al.  The critical Sobolev inequalities in Besov spaces and regularity criterion to some semi-linear evolution equations , 2002 .

[8]  R. Temam Navier-Stokes Equations , 1977 .

[9]  Hideo Kozono,et al.  Bilinear estimates in homogeneous Triebel‐Lizorkin spaces and the Navier‐Stokes equations , 2004 .

[10]  B. Jones,et al.  The initial value problem for the Navier-Stokes equations with data in Lp , 1972 .

[11]  Takehiko Ohyama,et al.  Interior regularity of weak solutions of the time-dependent Navier-Stokes equation , 1960 .

[12]  Pierre Gilles Lemarié-Rieusset,et al.  Multipliers between Sobolev spaces and fractional differentiation , 2006 .

[13]  Pierre Gilles Lemarié-Rieusset,et al.  The Navier-Stokes equations in the critical Morrey-Campanato space , 2007 .

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

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

[16]  Hyunseok Kim,et al.  Unique solvability for the density-dependent Navier–Stokes equations , 2004 .