8 research outputs found
Blow-up criteria for Boussinesq system and MHD system and Landau-Lifshitz equations in a bounded domain
In this paper, we prove some blow-up criteria for the 3D Boussinesq system
with zero heat conductivity and MHD system and Landau-Lifshitz equations in a
bounded domain.Comment: 20 page
On a parabolic logarithmic Sobolev inequality
In order to extend the blow-up criterion of solutions to the Euler equations,
Kozono and Taniuchi have proved a logarithmic Sobolev inequality by means of
isotropic (elliptic) norm. In this paper, we show a parabolic version of
the Kozono-Taniuchi inequality by means of anisotropic (parabolic) norm.
More precisely we give an upper bound for the norm of a function
in terms of its parabolic norm, up to a logarithmic correction involving
its norm in some Sobolev space. As an application, we also explain how to apply
this inequality in order to establish a long-time existence result for a class
of nonlinear parabolic problems