论文标题
大型轴对称解决方案的存在和渐近行为，用于稳定的Navier-Stokes系统
Existence and asymptotic behavior of large axisymmetric solutions for steady Navier-Stokes system in a pipe
论文作者
论文摘要
在本文中，即使外力在$ l^2 $中也适当大，在管道中稳定的纳维尔 - 斯托克斯系统具有较大通量的强轴对称解决方案的存在和唯一性。此外，只要外部力量在远场上呈指数融合，就确定了有限的$ h^2 $距离的任意稳定解决方案的指数收敛速率。获得这些大解决方案存在的关键点是沿流函数的轴向方向和漩涡速度的衍生物的精制估计，这利用了对流项的良好效果。对通用解决方案的渐近行为的一个重要观察结果是，当远处的$ h^2 $距离与哈根·波西乌尔流动时，这些解决方案实际上在遥远的领域很小。这使得对线性问题的估计值在研究远场的通用解决方案的收敛中起着至关重要的作用。
In this paper, the existence and uniqueness of strong axisymmetric solutions with large flux for the steady Navier-Stokes system in a pipe are established even when the external force is also suitably large in $L^2$. Furthermore, the exponential convergence rate at far fields for the arbitrary steady solutions with finite $H^2$ distance to the Hagen-Poiseuille flows is established as long as the external forces converge exponentially at far fields. The key point to get the existence of these large solutions is the refined estimate for the derivatives in the axial direction of the stream function and the swirl velocity, which exploits the good effect of the convection term. An important observation for the asymptotic behavior of general solutions is that the solutions are actually small at far fields when they have finite $H^2$ distance to the Hagen-Poiseuille flows. This makes the estimate for the linearized problem play a crucial role in studying the convergence of general solutions at far fields.
