Two-dimensional incompressible micropolar fluid models with singular initial data

Abstract

This paper deals with the interaction between microstructures and the appearance or persistence of singular configurations in the Cauchy problem for the two-dimensional model of incompressible micropolar fluids. We analyze the case of null angular viscosity and singular initial data, including the possibility of vortex sheets or measures as initial data in Morrey spaces. Through integral techniques we establish the existence of weak solutions local or global in time. In addition, the uniqueness and stability of these solutions is analyzed.