论文标题
固定轴向对称的Navier-Stokes方程的广义D-溶液的渐近特性
Asymptotic properties of generalized D-solutions to the stationary axially symmetric Navier-Stokes equations
论文作者
论文摘要
在本文中，我们将速度和涡度字段的渐近特性引导到Infinity的3维轴向对称的Navier-Stokes方程，该方程是在广义的D-Solutive假设$ \ int _ {\ int _ {\ MathBb {\ MathBb {r}^3}^3}^3} | \ nabla u |^qdx <\ f. $ 2 $ 2 <q <q <我们不会在无穷大的溶液上施加任何零或非恒定恒定矢量渐近假设。我们的结果概括了\ cite {cj：2009jmfm，ws：2018jmfm，cpz2018}中的结果，其中作者专注于案例$ q = 2 $，而速度字段接近无限。同时，当$ q \ to 2 _+$且速度字段接近无穷大时，我们的结果与\ cite {cj：2009jmfm，ws：2018jmfm，cpz2018}中的结果一致。
In this paper, we derive asymptotic properties of both the velocity and the vorticity fields to the 3-dimensional axially symmetric Navier-Stokes equations at infinity under the generalized D-solution assumption $\int_{\mathbb{R}^3}|\nabla u|^qdx<\infty$ for $2<q<\infty$. We do not impose any zero or nonzero constant vector asymptotic assumption on the solution at infinity. Our results generalize those in \cite{CJ:2009JMFM,Ws:2018JMFM,CPZ2018} where the authors focused on the case $q=2$ and the velocity field approaches zero at infinity. Meanwhile, when $q\to 2_+$ and the velocity field approaches zero at infinity, our results coincide with the results in \cite{CJ:2009JMFM,Ws:2018JMFM,CPZ2018}.
