| Journal Title /掲載ジャーナル名 |
Advances in Nonlinear Analysis |
| Publication Year and Month /掲載年月 |
January, 2023 |
| Paper Title /論文タイトル |
Stability of stationary solutions to the three-dimensional Navier-Strokes equations with surface tension |
| DOI /論文DOI |
10.1515/anona-2022-0279 |
| Author of Waseda University /本学の著者 |
WATANABE, Keiichi(Assistant Professor(without tenure), Faculty of Science and Engineering, Global Center for Science and Engineering):First Author, Corresponding Author, Last Author |
| Related Websites /関連Web |
– |
| Abstract /抄録 |
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 R3 , 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 Lp -in-time and Lq -in-space setting with (p,q)∈(2,∞)×(3,∞) satisfying 2/p+3/q<1 , where the solution becomes real analytic, jointly in time and space. It is also proved that the solution converges exponentially to the equilibrium. |
