Well-posedness and long time behavior for the electron inertial Hall-MHD system in Besov and Kato-Herz spaces

[摘要] In this paper, we study the wellposedness of the Hall-magnetohydrodynamic system augmented by the effect of electron inertia. Our main result consists of generalizing the wellposedness one in [17] from the Sobolev context to the general Besov spaces and Kato-Herz space. Then, we show that we can reduce the required regularity of the magnetic field in the first result modulo an additional condition on the maximal time of existence. Finally, we show that, for all p is an element of(3, infinity), the (L) over cap (p) (and eventually the L-p) norm of the solution (u, B, del x B), associated to small initial data in (B) over cap (3/p-1)(p,infinity)(R-3), is controlled by t(-1/2(1-3/p)), which provides a polynomial decay to zero of the (L) over cap (p) norm of the solution. (C) 2021 Elsevier Inc. All rights reserved.

[发布日期] 2021-09-15

[关键词] Hall-MHD system;MHD equations;Littlewood-Paley;Critical spaces;Long time behavior