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. (1st December 2022)

• Record Type: Journal Article
• Authors: Gu, Xumin; Luo, Chenyun; Zhang, Junyan
• Is Part Of: Nonlinearity. Volume 35:Number 12(2022)
• Page Start: 6349
• Page End: 6398
• Publication Date: 2022-12-01
• Subjects: free-boundary problems -- magnetohydrodynamics -- surface tension -- inviscid fluids; 35Q35 -- 76B45 -- 76W05; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/ac9a2f
• Languages: English
• ISSNs: 0951-7715

Abstract

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.