Stability of stationary solutions to the three-dimensional Navier-Stokes equations with surface tension

This article studies the stability of a stationary solution to the three-dimensional Navier-Stokes equations in a bounded domain, where surface tension effects are taken into account. More precisely, this article considers the stability of equilibrium figure of uniformly rotating viscous incompressi...

Full description

Saved in:
Bibliographic Details
Published in:Advances in nonlinear analysis 2023-01, Vol.12 (1), p.37-50
Main Author: Watanabe, Keiichi
Format: Article
Language:English
Subjects:
76D05
free boundary problems
maximal regularity
Navier-Stokes equations
Primary: 35R35
Secondary: 76D03
stability
surface tension
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:This article studies the stability of a stationary solution to the three-dimensional Navier-Stokes equations in a bounded domain, where surface tension effects are taken into account. More precisely, this article considers the stability of equilibrium figure of uniformly rotating viscous incompressible fluid in , which are rotationally symmetric about a certain axis. It is proved that this stability result can be obtained by the positivity of the second variation of the energy functional associated with the equation that determines an equilibrium figure, provided that initial data are close to an equilibrium state. The unique global solution is constructed in the -in-time and -in-space setting with satisfying , where the solution becomes real analytic, jointly in time and space. It is also proved that the solution converges exponentially to the equilibrium.
ISSN:2191-950X
2191-950X
DOI:10.1515/anona-2022-0279