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In this work we investigate the existence and uniqueness of Struwe-likesolutions for a system of partial differential equations modeling the dynamicsof magnetoviscoelastic fluids. The considered system couples a Navier-Stokestype equation with a dissipative equation for the deformation tensor and aLandau-Lifshitz-Gilbert type equation for the magnetization field. The mainpurpose is to establish a well-posedness theory in a two-dimensional periodicdomain under standard assumption of critical regularity for the (possiblylarge) initial data. We prove that the considered weak solutions are everywheresmooth, except for a discrete set of time values. The proof of the uniquenessis based on suitable energy estimates for the solutions within a functionalframework which is less regular than the one of the Struwe energy level. Theseestimates rely on several techniques of harmonic analysis and paradifferentialcalculus.

Struwe-like solutions for an evolutionary model of magnetoviscoelastic fluids