TY - JOUR
T1 - Long Time Well-Posedness of the MHD Boundary Layer Equation in Sobolev Space
AU - Chen , Dongxiang
AU - Ren , Siqi
AU - Wang , Yuxi
AU - Zhang , Zhifei
JO - Analysis in Theory and Applications
VL - 1
SP - 1
EP - 18
PY - 2020
DA - 2020/05
SN - 36
DO - http://doi.org/10.4208/ata.OA-0015
UR - https://global-sci.org/intro/article_detail/ata/16910.html
KW - MHD boundary layer equation, Sobolev space, well-posedness.
AB - <p style="text-align: justify;">In this paper, we study the long time well-posedness of 2-D MHD boundary layer equation. It was proved that if the initial data satisfies</p><p style="text-align: justify;">$$\|(u_0,h_0-1)\|_{H_{\mu}^{3,0}\cap H_{\mu}^{1,2}}\le \varepsilon,$$ then the life span of the solution is at least of order $\varepsilon^{2-\eta}$ for $\eta&gt;0$.</p>