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# 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: http://dx.doi.org/10.4310/CMS.2015.v13.n1.a11

#### Authors

#### 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

Published 16 July 2014