Struwe-like solutions for an evolutionary model of magnetoviscoelastic fluids

Abstract

In this work we investigate the existence and uniqueness of Struwe-like solutions for a system of partial differential equations modeling the dynamics of magnetoviscoelastic fluids. The considered system couples a Navier-Stokes type equation with a dissipative equation for the deformation tensor and a Landau–Lifshitz–Gilbert type equation for the magnetization field.The main purpose is to establish a well-posedness theory in a two-dimensional periodic domain under standard assumption of critical regularity for the (possibly large) initial data. We prove that the considered weak solutions are everywhere smooth, except for a discrete set of time values.The proof of the uniqueness is based on suitable energy estimates for the solutions within a functional framework which is less regular than the one of the Struwe energy level. These estimates rely on several techniques of harmonic analysis and paradifferential calculus.