We consider the magnetohydrodynamics system with Hall effect accompanied with initial data in supercritical Sobolev space. Via an appropriate randomization of the supercritical initial data, both local and small data global well-posedness for the system are obtained almost surely in critical Sobolev space.
Almost sure well-posedness for Hall MHD*
Mimi Dai, Institute for Advanced Study / University of Illinois at Chicago
2022 AWM Research Symposium
Deterministic and Probabilistic Approaches for Nonlinear PDEs