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2017 Remarks on regularity criteria for 2D generalized MHD equations
Zhuan Ye
Rocky Mountain J. Math. 47(4): 1333-1353 (2017). DOI: 10.1216/RMJ-2017-47-4-1333

Abstract

In this paper, we establish two regularity criteria for the two-dimensional (2D) incompressible generalized magnetohydrodynamic (GMHD) equations in terms of only one quantity, namely, the current density $j=\nabla \times b$ or the vorticity $\omega =\nabla \times u$. More precisely, it is proved that, if one of the following holds true: \[ \int _{0}^{T}{\|j(t)\|_{\dot {B}_{\infty ,\,\infty }^{0}(\mathbb {R}^{2})}\,dt}\lt \infty , \] \[ \int _{0}^{T}{\|\omega (t)\|_{\dot {B}_{\infty ,\,\infty }^{0}(\mathbb {R}^{2})}\,dt}\lt \infty , \] then the solution $(u,\,b)$ actually remains regular on $[0, T ]$.

Citation

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Zhuan Ye. "Remarks on regularity criteria for 2D generalized MHD equations." Rocky Mountain J. Math. 47 (4) 1333 - 1353, 2017. https://doi.org/10.1216/RMJ-2017-47-4-1333

Information

Published: 2017
First available in Project Euclid: 6 August 2017

zbMATH: 1375.35068
MathSciNet: MR3689957
Digital Object Identifier: 10.1216/RMJ-2017-47-4-1333

Subjects:
Primary: 35B35, 35B65, 35Q35, 76D03

Rights: Copyright © 2017 Rocky Mountain Mathematics Consortium

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Vol.47 • No. 4 • 2017
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