On the initial boundary value problem for certain 2D MHD-$\alpha$ equations without velocity viscosity

Jitao  Liu

doi:10.3934/cpaa.2016.15.1179

Article Contents

2016, Volume 15, Issue 4: 1179-1191. Doi: 10.3934/cpaa.2016.15.1179

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On the initial boundary value problem for certain 2D MHD-$\alpha$ equations without velocity viscosity

Jitao Liu^1,

1.
Instituto de Matemática, Universidade Federal do Rio de Janeiro, Cidade Universitária - Ilha do Fundão, Caixa Postal 68530, 21941-909 Rio de Janeiro, RJ

Received: April 30, 2015

Revised: January 31, 2016

Published: June 2016

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Abstract

This paper is concerned with the initial boundary value problem of certain 2D MHD-$\alpha$ equations without velocity viscosity over a bounded domain with smooth boundary. We show that the equations have a unique global smooth solution $(u,b)$ for $W^{4,p}\times H^4$ initial data and physical boundary condition.

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Mathematics Subject Classification: 35Q35, 76D03.

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