Communications in Mathematical Sciences

Volume 13 (2015)

Number 1

Global weak solutions of 3D compressible micropolar fluids with discontinuous initial data and vacuum

Pages: 225 – 247

DOI: https://dx.doi.org/10.4310/CMS.2015.v13.n1.a11

Authors

Mingtao Chen (School of Mathematics and Statistics, Shandong University, Weihai, China)

Xinying Xu (School of Mathematical Sciences, Xiamen University, Xiamen, China)

Jianwen Zhang (School of Mathematical Sciences, Xiamen University, Xiamen, China)

Abstract

In this paper, we study the global existence of weak solutions to the Cauchy problem for three-dimensional equations of compressible micropolar fluids with discontinuous initial data. Here it is assumed that the initial energy is suitably small in $L^2$, that the initial density is bounded in $L^{\infty}$, and the gradients of initial velocity and microrotational velocity are bounded in $L^2$. Particularly, this implies that the initial data may contain vacuum states and the oscillations of solutions could be arbitrarily large. As a byproduct, we also prove the global existence of smooth solutions with strictly positive density and small initial-energy.

Keywords

compressible micropolar fluids, vacuum, large oscillation, global weak solution, large-time behavior

2010 Mathematics Subject Classification

35G25, 76B03, 76N10

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Published 16 July 2014