Geodesic
A regularity criterion for the 2D MHD and viscoelastic fluid equations
Zhuan Ye1
1School of Mathematical Sciences Beijing Normal University Laboratory of Mathematics and Complex Systems Ministry of Education Beijing 100875, People's Republic of China
Annales Polonici Mathematici, Tome 114 (2015) no. 2, pp. 123-131
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 $T$.
DOI : 10.4064/ap114-2-3
Keywords: paper dedicated regularity criterion mhd equations viscoelastic equations prove magnetic field respectively local deformation gradient satisfies nabla nabla mathbb leq infty corresponding local solution extended beyond time

Zhuan Ye  1

1 School of Mathematical Sciences Beijing Normal University Laboratory of Mathematics and Complex Systems Ministry of Education Beijing 100875, People's Republic of China 
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Zhuan Ye. A regularity criterion for the 2D MHD and viscoelastic fluid equations. Annales Polonici Mathematici, Tome 114 (2015) no. 2, pp. 123-131. doi: 10.4064/ap114-2-3

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