Analysis and PDE Seminar——Asymptotic stability of the physically reasonable solution for the Navier-Stokes equations in a two-dimensional exterior domain
主 题: Analysis and PDE Seminar——Asymptotic stability of the physically reasonable solution for the Navier-Stokes equations in a two-dimensional exterior domain
报告人: Yasunori Maekawa (Kyoto University)
时 间: 2018-03-12 15:00-16:00
地 点: Room 1303, Sciences Building No. 1
Abstract: The flow past an obstacle is a fundamental object in fluid mechanics.In 1967, R. Finn and D.R. Smith proved the existence and uniqueness of a stationary solution, called "the physically reasonable solution", to the Navier-Stokes equations in a two-dimensional exterior domain modeling this type of flows, when the Reynolds number is sufficiently small. The spatial decay structure of this solution has been studied in details and is well understood by now, while its stability remained an open problem due to difficulties specific to the two-dimensionality.
In this talk we show that the physically reasonable solution constructed by Finn and Smith is asymptotically stable with respect to small and well-localized initial perturbations. This is the first stability result for the physically reasonable solution in two-dimensional case.
