References & Citations
Mathematics > Analysis of PDEs
Title: Stability of Navier-Stokes equations with a free surface
(Submitted on 25 Apr 2024 (v1), last revised 28 Apr 2024 (this version, 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.
Submission history
From: Yunrui Zheng [view email][v1] Thu, 25 Apr 2024 12:59:58 GMT (26kb)
[v2] Sun, 28 Apr 2024 09:16:19 GMT (25kb)
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