A regularity criterion for the 2D MHD and viscoelastic fluid equations
Volume 114 / 2015
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 $T$.
