INHOMOGENEOUS INCOMPRESSIBLE HALL-MHD SYSTEM WITH BOUNDED DENSITY

Jin Tan (1) , Lan Zhang (2)

1 AGM - UMR 8088 - Analyse, Géométrie et Modélisation
2 WHUT - Wuhan University of Technology

In this paper, we are dedicated to the global-in-time existence and uniqueness issues of solutions for the inhomogeneous incompressible Hall-MHD system with merely bounded density. In three-dimensional case, assuming that the initial density is a small perturbation of a positive constant in the L^∞ norm, we prove global well-posedness for small initial velocity and magnetic fields in critical Besov spaces. Next, we consider the so-called 2.5 D flows for the inhomogeneous Hall-MHD system (that is 3D flows independent of the vertical variable), and establish the global existence of strong solutions by assuming only that the initial magnetic field is small in critical spaces and the initial density is bounded and bounded away from zero. Our proofs work for general physical parameters and strongly rely on a new formulation of the system with its Lagrangian formulation. Moreover, some new maximal regularity estimates for parabolic system with just bounded coefficients are developed.

Mots clés: 2010 Mathematics Subject Classification. 35D30; 35Q35; 76D05; 76W05 Inhomogeneous Hall-MHD system; discontinuous density; critical regularity; maximal regularity

Domaines: Equations aux dérivées partielles [math.AP]

Jin Tan, Lan Zhang. INHOMOGENEOUS INCOMPRESSIBLE HALL-MHD SYSTEM WITH BOUNDED DENSITY. 2022. ⟨hal-03787507v2⟩