標題: On time periodic solutions, asymptotic stability and bifurcations of Navier-Stokes equations
作者: Hsia, Chun-Hsiung
Jung, Chang-Yeol
Thien Binh Nguyen
Shiue, Ming-Cheng
應用數學系
Department of Applied Mathematics
公開日期: Feb-2017
摘要: In this article, we investigate the time periodic solutions for two-dimensional Navier-Stokes equations with nontrivial time periodic force terms. Under the time periodic assumption of the force term, the existence of time periodic solutions for two-dimensional Navier-Stokes equations has received extensive attention from many authors. With the smallness assumption of the time periodic force, we show that there exists only one time periodic solution and this time periodic solution is globally asymptotically stable in the sense. Without smallness assumption of the force term, there is no stability analysis theory addressed. It is expected that when the amplitude of the force term is increasing, the time periodic solution is no longer asymptotically stable. In the last part of the article, we use numerical experiments to study the bifurcation of the time periodic solutions when the amplitude of the force is increasing. Extrapolating to the heating of the earth by the sun, the bifurcation diagram hints that when the earth receives a relatively small amount of solar energy regularly, the time periodic fluid patterns are asymptotically stable; while/when the earth receives too much solar energy even though in a time periodic way, the time periodic pattern of the fluid motions will lose its stability.
URI: http://dx.doi.org/10.1007/s00211-016-0812-3
http://hdl.handle.net/11536/133024
ISSN: 0029-599X
DOI: 10.1007/s00211-016-0812-3
期刊: NUMERISCHE MATHEMATIK
Volume: 135
Issue: 2
起始頁: 607
結束頁: 638
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