Zero surface tension limit of the free-boundary problem in incompressible magnetohydrodynamics* *XG was supported in part by NSFC Grant 12031006. CL was supported in part by the RGC Grant of Hong Kong CUHK-24304621 and CUHK Direct Grant for Research No. 4053457.

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 initially. This result is a continuation of the authors’ previous works (Gu et al 2020 arXiv:2105.00596; Gu and Wang 2019 J. Math. Pures Appl. 128 1–41; Luo and Zhang 2021 SIAM J. Math. Anal. 53 2595–630). Our proof is based on the combination of the techniques developed in our previous works (Gu et al 2020 arXiv:2105.00596; Gu and Wang 2019 J. Math. Pures Appl. 128 1–41; Luo and Zhang 2021 SIAM J. Math. Anal. 53 2595–630), Alinhac good unknowns, and a crucial anti-symmetric structure on the boundary.