A priori Estimates for the Incompressible Free-Boundary Magnetohydrodynamics Equations with Surface Tension

Chenyun Luo; Junyan Zhang

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A priori Estimates for the Incompressible Free-Boundary Magnetohydrodynamics Equations with Surface Tension

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arxiv 1907.11827 v3 pith:IKWZINF7 submitted 2019-07-27 math.AP

Chenyun Luo , Junyan Zhang This is my paper

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keywords surfacetensionequationsfree-boundaryincompressibleboundarymagnetohydrodynamicspriori

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abstract

We consider the three-dimensional incompressible free-boundary magnetohydrodynamics (MHD) equations in a bounded domain with surface tension on the boundary. We establish a priori estimate for solutions in the Lagrangian coordinates with $H^{3.5}$ regularity. To the best of our knowledge, this is the first result focusing on the incompressible ideal free-boundary MHD equations with surface tension. It is worth pointing out that the $1/2$-extra spatial regularity for the flow map $\eta$ is no longer required in this manuscript thanks to the presence of the surface tension on the boundary.

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