论文标题
不可压缩的Navier-Stokes方程和应用到轴对称解决方案的加权能量估计值
Weighted energy estimates for the incompressible Navier-Stokes equations and applications to axisymmetric solutions without swirl
论文作者
论文摘要
我们考虑了一个允许概括Leray程序的重量家族，以获得3D不可用的Navier-Stokes方程的弱解决方案，并在加权L 2个空间中具有初始数据。当初始速度是轴对称矢量场而没有漩涡的情况下，我们的主要结果涉及常规全局溶液的存在，使得初始速度及其涡度均属于L 2（（1 + r 2） - $γ$ 2 dx），r = x 2 1 + x 2 2 2和$γ$ \ $ \ in $ in $ in $ in $（0，2）。
We consider a family of weights which permit to generalize the Leray procedure to obtain weak suitable solutions of the 3D incom-pressible Navier-Stokes equations with initial data in weighted L 2 spaces. Our principal result concerns the existence of regular global solutions when the initial velocity is an axisymmetric vector field without swirl such that both the initial velocity and its vorticity belong to L 2 ((1 + r 2) -- $γ$ 2 dx), with r = x 2 1 + x 2 2 and $γ$ $\in$ (0, 2).
