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<p>We construct in the paper the low-regularity strong solutions to the viscous surface wave equations in anisotropic Sobolev spaces. By using the Lagrangian structure of the system to homogenize the free boundary conditions coupled with the semigroup method of the linear operator, we establish a new iteration scheme on a known equilibrium domain to get the low-regularity strong solutions, in which no compatibility conditions of the accelerated velocity on the initial data are required.</p>

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Construction of Low Regularity Strong Solutions to the Viscous Surface Wave Equations

  • 期刊论文

  • 发表日期：

    2025年4月23日

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  • Guilong Gui,
  • Yancan Li

摘要

We construct in the paper the low-regularity strong solutions to the viscous surface wave equations in anisotropic Sobolev spaces. By using the Lagrangian structure of the system to homogenize the free boundary conditions coupled with the semigroup method of the linear operator, we establish a new iteration scheme on a known equilibrium domain to get the low-regularity strong solutions, in which no compatibility conditions of the accelerated velocity on the initial data are required.