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-infinity, 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 by product, we also prove the global existence of smooth solutions with strictly positive density and small initial-energy.
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