Asymptotic behavior of solutions of the stationary Navier-Stokes equations in an exterior domain

2010/08/24 by Ching-Lung Lin, Günther Uhlmann, Lin, Ching-Lung +3
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.1008.3953

openalex publication_date 2010/08/24 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We study the asymptotic behavior of an incompressible fluid around a bounded obstacle. The problem is modeled by the stationary Navier-Stokes equations in an exterior domain in \Rⁿ with n≥ 2. We will show that, under some assumptions, any nontrivial velocity field obeys a minimal decaying rate exp(-Ct²log t) at infinity. Our proof is based on appropriate Carleman estimates.

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