Well-posedness for the Linearized Free Boundary Problem of Incompressible Ideal Magnetohydrodynamics Equations
arXiv:1912.05908 · doi:10.1016/j.jde.2021.07.030
Abstract
We study the well-posedness theory for the linearized free boundary problem of incompressible ideal magnetohydrodynamics equations in a bounded domain. We express the magnetic field in terms of the velocity field and the deformation tensors in the Lagrangian coordinates, and substitute the magnetic field into the momentum equation to get an equation of the velocity in which the initial magnetic field serves only as a parameter. Then, we linearize this equation with respect to the position vector field whose time derivative is the velocity, and obtain the local-in-time well-posedness of the solution by using energy estimates of the tangential derivatives and the curl with the help of Lie derivatives and the smooth-out approximation.
54 pages. Update references. arXiv admin note: text overlap with arXiv:math/0112030 by other authors
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Cited by in corpus (6)
- Zero Surface Tension Limit of the Free-Boundary Problem in Incompressible Magnetohydrodynamics
- Local Well-posedness of the Free-Boundary Incompressible Magnetohydrodynamics with Surface Tension
- Local Well-posedness of the Free-Boundary Problem in Compressible Resistive Magnetohydrodynamics
- Anisotropic Regularity of the Free-Boundary Problem in Compressible Ideal Magnetohydrodynamics
- A priori Estimates for the Free-Boundary problem of Compressible Resistive MHD Equations and Incompressible Limit
- Well-posedness for moving interfaces in anisotropic plasmas