论文标题
稳定的Navier-Stokes系统的Liouville型定理的相对衰减条件
Relative decay conditions on Liouville type theorem for the steady Navier-Stokes system
论文作者
论文摘要
在本文中，我们证明了liouville定理在$ \ bbb r^3 $中以速度，压力和头部压力的相对衰减的假设为$ \ bbb r^3 $。更确切地说，我们表明，任何平滑的解决方案$（u，p）$ sentary navier-stokes方程满足$ u（x）\ to 0 $ as $ | x | \ to +\ to +\ to +\ infty $和有限的dirichlet intectal $ \ int $ \ int _ {\ bb bb r^3} | \ nabla u |^2 dx <+\ infty $是微不足道的，如果$ | u |/| q | = o（1）$或$ | p |/| q | = o（1）$ as $ | x | \ to \ infty $，其中$ | q | = \ frac12 | u |^2 +p $是头压力。
In this paper we prove Liouville type theorem for the stationary Navier-Stokes equations in $\Bbb R^3$ under the assumptions on the relative decays of velocity, pressure and the head pressure. More precisely, we show that any smooth solution $(u,p)$ of the stationary Navier-Stokes equations satisfying $u(x) \to 0$ as $|x|\to +\infty$ and the condition of finite Dirichlet integral $\int_{\Bbb R^3} | \nabla u|^2 dx <+\infty $ is trivial, if either $|u|/|Q|=O(1)$ or $|p|/|Q| =O(1) $ as $|x|\to \infty$, where $|Q|=\frac12 |u|^2 +p$ is the head pressure.
