Well-posedness for the incompressible Hall-MHD system with initial magnetic field belonging to $H^{\frac{3}{2}}(\mathbb{R}^3)$

DOI10.1007/S00021-023-00766-YarXiv2108.09599MaRDI QIDQ6375751

Publication date: 21 August 2021

Abstract: In this paper, we first prove the local well-posedness of strong solutions to the incompressible Hall-MHD system for initial data

(u_{0}, B_{0}) i n H^{f r a c 12 + s i g m a} (m a t h b b R^{3}) i m e s H^{f r a c 32} (m a t h b b R^{3})

with

s i g m a i n (0, 2)

. In particular, if the viscosity coefficient is equal to the resistivity coefficient, we can reduce

s i g m a

to

0

with the aid of the new formulation of the Hall-MHD system observed by Danchin and Tan (Commun Partial Differ Equ 46(1):31-65, 2021). Compared with the previous works, our local well-posedness results improve the regularity condition on the initial data. Moreover, we establish the global well-posedness for small initial data in

H^{f r a c 12 + s i g m a} (m a t h b b R^{3}) i m e s H^{f r a c 32} (m a t h b b R^{3})

with

s i g m a i n (0, 2)

, and get the optimal time-decay rates of solutions.

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Asymptotic behavior of solutions to PDEs (35B40) PDEs in connection with fluid mechanics (35Q35) Magnetohydrodynamics and electrohydrodynamics (76W05) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Existence, uniqueness, and regularity theory for incompressible viscous fluids (76D03) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Strong solutions to PDEs (35D35)

This page was built for publication: Well-posedness for the incompressible Hall-MHD system with initial magnetic field belonging to $H^{\frac{3}{2}}(\mathbb{R}^3)$

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q6375751)