Zero Surface Tension Limit of the Free-Boundary Problem in Incompressible Magnetohydrodynamics
arXiv:2109.05400 · doi:10.1088/1361-6544/ac9a2f
Abstract
We show that the solution of the free-boundary incompressible ideal magnetohydrodynamic (MHD) equations with surface tension converges to that of the free-boundary incompressible ideal MHD equations without surface tension given the Rayleigh-Taylor sign condition holds true initially. This result is a continuation of the authors' previous works [17,32,16]. Our proof is based on the combination of the techniques developed in our previous works [17,32,16], Alinhac good unknowns, and a crucial anti-symmetric structure on the boundary.
35 pages. Final version, accepted by Nonlinearity. We extend the result to the case of a general diffeomorphism
References in corpus (5)
- The Magnetic Rayleigh-Taylor Instability in Three Dimensions
- Nonlinear Evolution of the Magnetohydrodynamic Rayleigh-Taylor Instability
- Well-Posedness for the Free-Boundary Ideal Compressible Magnetohydrodynamic Equations with Surface Tension
- A Lagrangian Interior Regularity Result for the Incompressible Free Boundary Euler Equation with Surface Tension
- Well-posedness of axially symmetric incompressible ideal magnetohydrodynamic equations with vacuum under the Rayleigh-Taylor sign condition