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.