This research establishes global well-posedness for the free boundary problem in incompressible viscous MHD, suggesting critical conditions for linearized equations.
Key Points
A unique global solution exists under small initial data norm in critical Besov space.
Maximal L1-regularity is established for Stokes equations and linearized magnetic field equations.
Existence and uniqueness of solutions are proven using the Banach contraction mapping principle.
Research builds on previous work in the half-space setting to enhance mathematical understanding.