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arXiv · 1912.09194

The Global Solvability Of The Hall-magnetohydrodynamics System In Critical Sobolev Spaces

Raphaël Danchin·Jin Tan
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Abstract

We are concerned with the 3D incompressible Hall-magnetohydro-dynamic system (Hall-MHD). Our first aim is to provide the reader with an elementary proof of a global well-posedness result for small data with critical Sobolev regularity, in the spirit of Fujita-Kato's theorem [10] for the Navier-Stokes equations. Next, we investigate the long-time asymptotics of global solutions of the Hall-MHD system that are in the Fujita-Kato regularity class. A weak-strong uniqueness statement is also proven. Finally, we consider the so-called 2 1/2 D flows for the Hall-MHD system, and prove the global existence of strong solutions, assuming only that the initial magnetic field is small.

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Raphaël Danchin, Jin Tan. 2019-12-19. The Global Solvability Of The Hall-magnetohydrodynamics System In Critical Sobolev Spaces. https://arxiv.org/abs/1912.09194

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