论文标题
渐近边界条件的无限圆柱体外部的轴对称固定纳维尔 - 长方形方程的渐近行为和liouville型定理
Asymptotic behavior and Liouville-type theorems for axisymmetric stationary Navier-Stokes equations outside of an infinite cylinder with a periodic boundary condition
论文作者
论文摘要
我们研究$ \ Mathbb {r}^3 $的无限缸外稳定的Navier-Stokes方程的解决方案的渐近行为。我们假设该流量为$ x_3 $ - 方向是周期性的，没有旋流。这个问题与二维外部问题密切相关。在广义有限的Dirichlet积分的条件下，我们给出了空间无穷大的涡度的点衰减估计。此外，我们仅根据广义有限的Dirichlet积分的条件才能证明Liouville型定理。
We study the asymptotic behavior of solutions to the steady Navier-Stokes equations outside of an infinite cylinder in $\mathbb{R}^3$. We assume that the flow is periodic in $x_3$-direction and has no swirl. This problem is closely related with two-dimensional exterior problem. Under a condition on the generalized finite Dirichlet integral, we give a pointwise decay estimate of the vorticity at the spatial infinity. Moreover, we prove a Liouville-type theorem only from the condition of the generalized finite Dirichlet integral.
