solidot新版网站常见问题,请点击这里查看。
消息
本文已被查看18694次
Convergence of filtered weak solutions to the 2D Euler equations with vortex sheet initial data. (arXiv:1810.09636v1 [math.AP])
来源于:arXiv
We study weak solutions of the two-dimensional (2D) filtered Euler equations
whose vorticity is a finite Radon measure and velocity has locally finite
kinetic energy, which is called the vortex sheet solution. The 2D filtered
Euler equations are considered as a regularized 2D Euler equations with a
spatial filtering and these equations have a unique global weak solution for
vortex sheet initial data. On the other hand, the 2D Euler equations require a
distinguished sign of initial vorticity for the existence of a global solution
with vortex sheet initial data and its uniqueness remains an open question. In
this paper, we prove that vortex sheet solutions of the 2D filtered Euler
equations converge to those of the 2D Euler equations in the limit of the
filtering parameter provided that initial vortex sheet has a distinguished
sign. We also show that a simple application of our proof yields the
convergence of the vortex method that is a point vortex approximation of vortex
sheets. We mak 查看全文>>