arrow
Volume 36, Issue 1
Long Time Well-Posedness of the MHD Boundary Layer Equation in Sobolev Space

Dongxiang Chen, Siqi Ren, Yuxi Wang & Zhifei Zhang

Anal. Theory Appl., 36 (2020), pp. 1-18.

Published online: 2020-05

[An open-access article; the PDF is free to any online user.]

Export citation
  • Abstract

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

$$\|(u_0,h_0-1)\|_{H_{\mu}^{3,0}\cap H_{\mu}^{1,2}}\le \varepsilon,$$ then the life span of the solution is at least of order $\varepsilon^{2-\eta}$ for $\eta>0$.

  • AMS Subject Headings

35Q30, 76D03

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

chendx020@aliyun.com (Dongxiang Chen)

zfzhang@math.pku.edu.cn (Zhifei Zhang)

  • BibTex
  • RIS
  • TXT
@Article{ATA-36-1, author = {Chen , DongxiangRen , SiqiWang , Yuxi and Zhang , Zhifei}, title = {Long Time Well-Posedness of the MHD Boundary Layer Equation in Sobolev Space}, journal = {Analysis in Theory and Applications}, year = {2020}, volume = {36}, number = {1}, pages = {1--18}, abstract = {

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

$$\|(u_0,h_0-1)\|_{H_{\mu}^{3,0}\cap H_{\mu}^{1,2}}\le \varepsilon,$$ then the life span of the solution is at least of order $\varepsilon^{2-\eta}$ for $\eta>0$.

}, issn = {1573-8175}, doi = {https://doi.org/10.4208/ata.OA-0015}, url = {http://global-sci.org/intro/article_detail/ata/16910.html} }
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 -

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

$$\|(u_0,h_0-1)\|_{H_{\mu}^{3,0}\cap H_{\mu}^{1,2}}\le \varepsilon,$$ then the life span of the solution is at least of order $\varepsilon^{2-\eta}$ for $\eta>0$.

Dongxiang Chen, Siqi Ren, Yuxi Wang & Zhifei Zhang. (2020). Long Time Well-Posedness of the MHD Boundary Layer Equation in Sobolev Space. Analysis in Theory and Applications. 36 (1). 1-18. doi:10.4208/ata.OA-0015
Copy to clipboard
The citation has been copied to your clipboard