Well-posedness for magnetoviscoelastic fluids in 3D. (February 2023)

• Record Type: Journal Article
• Authors: Du, Hengrong; Shao, Yuanzhen; Simonett, Gieri
• Is Part Of: Nonlinear analysis. Volume 69(2023)
• Publication Date: 2023-02
• Subjects: Landau–Lifshitz–Gilbert system -- Quasilinear parabolic equation -- Strong well-posedness -- Normally stable -- Lyapunov function -- Convergence to equilibria; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2022.103759
• Languages: English
• ISSNs: 1468-1218

Abstract

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