Abstract
<abstract><p>In this work, we investigated the local existence of the solutions to the 2D magnetohy-drodynamic (MHD) boundary layer equations on the half plane by energy methods in weighted Sobolev space. Compared to the existence of solutions to the classical Prandtl equations where the monotonicity condition of the tangential velocity plays an important role, we used the initial tangential magnetic field with a lower bound $ \delta > 0 $ instead of the monotonicity condition of the tangential velocity.</p></abstract>
Publisher
American Institute of Mathematical Sciences (AIMS)
Reference31 articles.
1. R. A. Adams, J. J. F. Fournier, Sobolev Spaces, New York-London: Academic Press, 2003.
2. R. Alexandre, Y. G. Wang, C. J. Xu, T. Yang, Well-posedness of the Prandtl equation in Sobolev spaces, J. Am. Math. Soc., 28 (2015), 745–784. http://doi.org/10.1090/S0894-0347-2014-00813-4
3. T. G. Cowling, Magnetohydrodynamics, New York: Interscience Publishers Inc., 1957.
4. D. X. Chen, X. L. Li, Long time well-posedness of two dimensional Magnetohydrodynamic boundary layer equation without resistivity, Math. Method. Appl. Sci., 46 (2023), 10186–10202. http://doi.org/10.1002/mma.9110
5. P. A. Davidson, An introduction to magnetohydrodynamics, Cambridge: Cambridge University Press, 2001. https://doi.org/10.1017/CBO9780511626333