Well-posedness for magnetoviscoelastic fluids in 3D

We show that the system of equations describing a magnetoviscoelastic fluid in three dimensions can be cast as quasilinear parabolic system. Using theory maximal Lp-regularity, we establish existence and uniqueness local strong solutions each solution is smooth (in fact analytic) space time. Moreover, give complete characterization set equilibria start out close to constant equilibrium exist globally converge (possibly different) equilibrium. Finally, every eventually bounded topology state exists converges equilibria.