Note on global regularity of 3D generalized magnetohydrodynamic-$\alpha$ model with zerodiffusivity

Xiaojing Xu; Zhuan Ye

doi:10.3934/cpaa.2015.14.585

Article Contents

2015, Volume 14, Issue 2: 585-595. Doi: 10.3934/cpaa.2015.14.585

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Note on global regularity of 3D generalized magnetohydrodynamic-$\alpha$ model with zero diffusivity

Xiaojing Xu^1, and
Zhuan Ye^1,

1.
School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875

Received: May 31, 2014

Revised: July 31, 2014

Published: February 2015

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Abstract

In this paper we consider the Cauchy problem of a three-dimensional incompressible magnetohydrodynamic-$\alpha$ (MHD-$\alpha$) model with fractional velocity and zero magnetic diffusivity. We prove the global existence results of classical solutions for the model in the endpoint case with arbitrarily large initial data in Sobolev spaces.

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Mathematics Subject Classification: 35Q35, 76D03,.

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