TY - JOUR
T1 - Well-Posedness of MHD Equations in Sobolev-Gevery Space
AU - Liu , Qian
AU - Yuan , Baoquan
JO - Journal of Nonlinear Modeling and Analysis
VL - 2
SP - 320
EP - 332
PY - 2024
DA - 2024/06
SN - 6
DO - http://doi.org/10.12150/jnma.2024.320
UR - https://global-sci.org/intro/article_detail/jnma/23178.html
KW - MHD equation, Sobolev-Gevery space, well-posedness.
AB - <p style="text-align: justify;">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.</p>