【nba赌注平台】On Leray’s problem in an infinite long pipe with the Navier-slip boundary condition
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题目：On Leray’s problem in an infinite long pipe with the Navier-slip boundary condition
时 间: 2022年5月28日 上午9:30-10:30
方式: 腾讯会议 ID：113-791-963 会议密码：220528
摘要：The original Leray"s problem concerns the well-posedness of weak solutions to the steady incompressible Navier-Stokes equations in a distorted pipe, which approach to the Poiseuille flow subject to the no-slip boundary condition at spacial infinity. In this talk, the same problem with the Navier-slip boundary condition instead of the no-slip boundary condition, is addressed. Due to the complexity of the boundary condition, some new ideas, presented as follows, are introduced to handle the extra difficulties caused by boundary terms. First, the Poiseuille flow in the semi-infinite straight pipe with the Navier-slip boundary condition will be introduced, which will be served as the asymptotic profile of the solution to the generalized Leray"s problem at spacial infinity. Second, a solenoidal vector function defined in the whole pipe, satisfying the Navier-slip boundary condition, having the designated flux and equalling to the Poiseuille flow at large distance, will be carefully constructed. This plays an important role in reformulating our problem. Third, the energy estimates depend on a combined L^2 estimate of the gradient and the stress tensor of the velocity. This is a joint work with Zijin Li and Xinghong Pan.