题目：The Global Solvability of the Hall-Magneto-Hydrodynamics System in Critical Sobolev Spaces

报告人：谈进 博士 （巴黎十二大学） 

地点：腾讯会议室 (会议ID: 886 686 598)

时间：2021年6月16日（星期三） 16：00-17：00

摘要：In this talk, I will talk about our recent results for the well-posedness of the 3D incompressible Hall-magneto-hydrodynamic system (Hall-MHD). First, we provide an elementary proof of a global well-posedness result for small data with critical Sobolev regularity, in the spirit of Fujita-Kato’s theorem for the Navier-Stokes equations. Next, we present the long-time asymptotics of global (possibly large) solutions of the Hall-MHD system that are in the Fujita-Kato regularity class. A weak-strong uniqueness statement is also presented. Finally, we consider the so-called 2.5D flows for the Hall-MHD system (that is 3D flows independent of the vertical variable), and establish a global existence of strong solutions, assuming only that the initial magnetic field is small.

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