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研究员、博士生导师,中国科学院数学与系统科学研究院 数学研究所 | Professor, Institute of Mathematics, AMSS, CAS
A Priori Estimates for Free Boundary Problem of Incompressible Inviscid Magnetohydrodynamic Flows
Chengchun Hao, Tao Luo
Archive for Rational Mechanics and Analysis, Volume 212, Issue 3, pp 805-847, 2014. [PDF]
Abstract:In the present paper, we prove the a priori estimates of Sobolev norms for a free boundary problem of the incompressible inviscid magnetohydrodynamics equations in all physical spatial dimensions $n=2$ and $3$ by adopting a geometrical point of view used in Christodoulou and Lindblad (Commun Pure Appl Math 53:1536-1602, 2000), and estimating quantities such as the second fundamental form and the velocity of the free surface. We identify the well-posedness condition that the outer normal derivative of the total pressure including the fluid and magnetic pressures is negative on the free boundary, which is similar to the physical condition (Taylor sign condition) for the incompressible Euler equations of fluids.
http://link.springer.com/article/10.1007/s00205-013-0718-5