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Global existence of 2D nonhomogeneous incompressible magnetohydrodynamics with vacuum

Menglong Su1*, Xiaohui Qian2 and Jian Wang3

Author Affiliations

1 School of Mathematical Sciences, Luoyang Normal University, Luoyang, 471022, P.R. China

2 College of Science, Zhongyuan University of Technology, Zhengzhou, 450007, P.R. China

3 School of Mathematics, Ocean University of China, Qingdao, 266100, P.R. China

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Boundary Value Problems 2014, 2014:94  doi:10.1186/1687-2770-2014-94

Published: 6 May 2014

Abstract

In this paper, we prove the existence of global strong solutions to the Cauchy problem of 2D incompressible magnetohydrodynamics (MHD) flows. Here, we emphasize that the initial density <a onClick="popup('http://www.boundaryvalueproblems.com/content/2014/1/94/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2014/1/94/mathml/M1">View MathML</a> is permitted to contain vacuum states, and the initial velocity <a onClick="popup('http://www.boundaryvalueproblems.com/content/2014/1/94/mathml/M2','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2014/1/94/mathml/M2">View MathML</a> and magnetic fields <a onClick="popup('http://www.boundaryvalueproblems.com/content/2014/1/94/mathml/M3','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2014/1/94/mathml/M3">View MathML</a> can be arbitrarily large.

Keywords:
global strong solutions; 2D incompressible magnetohydrodynamics flows; vacuum states