Regularity and uniqueness of global solutions for the 3D compressible micropolar fluids

Abstract

This paper concerns the regularity and uniqueness of 3D compressible micropolar fluids in the whole space R3. We first establish some new Lp gradient estimates of the solutions for the system, then by virtue of the “div-rot” decomposition technique, the key estimates ‖∇u‖L3 and ‖∇w‖L3 are obtained. As a result, the existence and uniqueness of global solutions belonging to a new class of functions are obtained, provided the initial energy is suitable small. It is worth noting that compared with the existing results, this paper has lower regularity of initial data.