Regularity criteria for the solutions to the 3D MHD equations in the multiplier space

Article

Abstract

In this paper, some improved regularity criteria for the 3D viscous MHD equations are established in multiplier spaces. It is proved that if the velocity field satisfies
$$u \in L^{\frac{2}{1-r}}\left( 0,T,\overset{.}{X}_{r}(\mathbb{R}^{3}) \right) \quad {\rm with}\,r\in [0,1[,$$
or the gradient field of velocity satisfies
$$\nabla u\in L^{\frac{2}{2-\gamma}}\left(0,T,\overset{.}{X}_{\gamma}(\mathbb{R}^{3}) \right) \quad {\rm with}\,\gamma \in \left[ 0,1\right],$$
then the solution remains smooth on [0, T].

Mathematics Subject Classification (2000)

35Q35 35B65 76D05 

Keywords

MHD equations Regularity criterion A priori estimates 

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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2009

Authors and Affiliations

  1. 1.Department of MathematicsZhejiang Normal UniversityJinhuaPeople’s Republic of China
  2. 2.Department of MathematicsUniversity of MostaganemMostaganemAlgeria

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