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A regularity criterion for the 2D MHD and viscoelastic fluid equations

Volume 114 / 2015

Zhuan Ye Annales Polonici Mathematici 114 (2015), 123-131 MSC: Primary 35Q35, 76A10; Secondary 35B44. DOI: 10.4064/ap114-2-3

Abstract

This paper is dedicated to a regularity criterion for the 2D MHD equations and viscoelastic equations. We prove that if the magnetic field $B$, respectively the local deformation gradient $F$, satisfies $$\nabla B,\,\,\nabla F \in L^{q}(0,T; L^{p}(\mathbb{R}^{2}))$$ for ${1}/{p}+{1}/{q}=1$ and $2< p\leq \infty$, then the corresponding local solution can be extended beyond time $T$.

Authors

  • Zhuan YeSchool of Mathematical Sciences
    Beijing Normal University
    Laboratory of Mathematics and Complex Systems
    Ministry of Education
    Beijing 100875, People's Republic of China
    e-mail

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