Well-Posedness of MHD Equations in Sobolev-Gevery Space

Year:    2024

Author:    Qian Liu, Baoquan Yuan

Journal of Nonlinear Modeling and Analysis, Vol. 6 (2024), Iss. 2 : pp. 320–332

Abstract

This paper is devoted to the study of the 3D incompressible magnetohydrodynamic system. We prove the local in time well-posedness for any large initial data in $\dot{H}^1_{a,1}(\mathbb{R}^3)$ or $H^1_{a,1}(\mathbb{R}^3).$ Furthermore, the global well-posedness of a strong solution in $\tilde{L}^∞(0, T; H^1_{ a,1}(\mathbb{R}^3)) ∩ L^2 (0, T; \dot{H}^1_{a,1}(\mathbb{R}^3) ∩ \dot{H}^2_{a,1}(\mathbb{R}^3))$ with initial data satisfying a smallness condition is established.

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.12150/jnma.2024.320

Journal of Nonlinear Modeling and Analysis, Vol. 6 (2024), Iss. 2 : pp. 320–332

Published online:    2024-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    13

Keywords:    MHD equation Sobolev-Gevery space well-posedness.

Author Details

Qian Liu

Baoquan Yuan