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A Liouville theorem of Navier-Stokes equations with two periodic variables
Journal of Mathematical Analysis and Applications ( IF 1.3 ) Pub Date : 2020-05-01 , DOI: 10.1016/j.jmaa.2020.123854
Xinghong Pan

Abstract In this paper, we study the Liouville theorem of the stationary Navier-Stokes equations in R 3 . When the solution is periodic in two variables, we can prove that actually the solution is trivial (constant vector) under the assumption that one component of the velocity, vanishing at infinity, has finite Dirichlet integral and the other two components can have some growth with respect to the distance to the origin.

中文翻译:

具有两个周期变量的纳维-斯托克斯方程的刘维尔定理

摘要 本文研究了R 3 中平稳Navier-Stokes方程的Liouville定理。当解在两个变量中是周期性的时,我们可以证明实际上解是平凡的(恒定向量),假设速度的一个分量在无穷远处消失,具有有限的狄利克雷积分,而其他两个分量可以有一些增长关于到原点的距离。
更新日期:2020-05-01
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