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<p>In this paper, we consider the three-dimensional incompressible free-boundary magnetohydrodynamics (MHD) equations in a bounded domain involving a free moving surface boundary with surface tension. We derive the a priori estimate for solutions under minimal regularity assumptions on the initial data in Lagrangian coordinates. To the best of our knowledge, this seems to be the first attempt to establish the result of low regularity solution for incompressible free-boundary MHD equations with surface tension. Such result extends the works of Luo and Zhang [SIAM, 53 (2021), pp. 2595-2630] and Disconzi, Kukavica and Tuffaha [SIAM, 51 (2019), pp. 3982-4022].</p>

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A Lagrangian Interior Regularity Result for the Incompressible Free Boundary Magnetohydrodynamics Equations with Surface Tension

  • 期刊论文

  • 发表日期：

    2026年7月1日

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  • Zhi Chen,
  • Weixun Feng,
  • Dongdong Qin,
  • Fan Wu

摘要

In this paper, we consider the three-dimensional incompressible free-boundary magnetohydrodynamics (MHD) equations in a bounded domain involving a free moving surface boundary with surface tension. We derive the a priori estimate for solutions under minimal regularity assumptions on the initial data in Lagrangian coordinates. To the best of our knowledge, this seems to be the first attempt to establish the result of low regularity solution for incompressible free-boundary MHD equations with surface tension. Such result extends the works of Luo and Zhang [SIAM, 53 (2021), pp. 2595-2630] and Disconzi, Kukavica and Tuffaha [SIAM, 51 (2019), pp. 3982-4022].