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Open Access Research

Blow-up criterion for 3D compressible viscous magneto-micropolar fluids with initial vacuum

Peixin Zhang

Author Affiliations

School of Mathematical Sciences, Huaqiao University, Quanzhou, 362021, P.R. China

Boundary Value Problems 2013, 2013:160  doi:10.1186/1687-2770-2013-160

Published: 1 July 2013

Abstract

In this paper, the author establishes a blow-up criterion of strong solutions to 3D compressible viscous magneto-micropolar fluids. It is shown that if the density and the velocity satisfy <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/160/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/160/mathml/M1">View MathML</a>, where <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/160/mathml/M2','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/160/mathml/M2">View MathML</a> and <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/160/mathml/M3','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/160/mathml/M3">View MathML</a>, then the strong solutions to the Cauchy problem can exist globally over <a onClick="popup('http://www.boundaryvalueproblems.com/content/2013/1/160/mathml/M4','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2013/1/160/mathml/M4">View MathML</a>. The initial density may vanish on open sets, that is, the initial vacuum is allowed.

MSC: 76N10, 35B44, 35B45.

Keywords:
compressible magneto-micropolar fluids; blow-up criterion; strong solution; vacuum