Stability of Navier-Stokes equations with a free surface
Analysis of PDEs
2024-04-30 v2
Abstract
We consider the viscous incompressible fluids in a three-dimensional horizontally periodic domain bounded below by a fixed smooth boundary and above by a free moving surface. The fluid dynamics are governed by the Navier-Stokes equations with the effect of gravity and surface tension on the free surface. We develop a global well-posedness theory by a nonlinear energy method in low regular Sobolev spaces with several techniques, including: the horizontal energy-dissipation estimates, a new tripled bootstrap argument inspired by Guo and Tice [Arch. Ration. Mech. Anal.(2018)]. Moreover, the solution decays asymptotically to the equilibrium in an exponential rate.
Cite
@article{arxiv.2404.16585,
title = {Stability of Navier-Stokes equations with a free surface},
author = {Xing Cheng and Yunrui Zheng},
journal= {arXiv preprint arXiv:2404.16585},
year = {2024}
}