Almost sure well-posedness for Hall MHD

2022/02/09 by Dai, Mimi
#35Q35 #76D03 #76W05 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2202.04265

Abstract

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.

Related

• The Global Solvability Of The Hall-magnetohydrodynamics System In Critical Sobolev Spaces
• Local well-posedness for the Hall-MHD system in optimal Sobolev Spaces
• Global well-posedness for the Hall-magnetohydrodynamics system in larger critical Besov spaces
• On the blow-up criterion and small data global existence for the Hall-magnetohydrodynamics
• Local well-posedness of the Hall-MHD system in H^s(\mathbb Rⁿ) with s>\frac n2