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Open Access Research

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


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.

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