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arXiv · 2404.08448

Construction of low regularity strong solutions to the viscous surface wave equations

Guilong Gui·Yancan Li
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Abstract

We construct in the paper the low-regularity strong solutions to the viscous surface wave equations in anisotropic Sobolev spaces. Here we use the Lagrangian structure of the system to homogenize the free boundary conditions, and establish a new iteration scheme on a known equilibrium domain to get the low-regularity strong solutions, in which no nonlinear compatibility conditions on the initial data are required.

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Guilong Gui, Yancan Li. 2024-04-12. Construction of low regularity strong solutions to the viscous surface wave equations. https://arxiv.org/abs/2404.08448

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