Asymptotic stability for viscous fluid motion in exterior domains
Some asymptotic stability results for Navier-Stokes fluid filling an exterior domain are shown in this paper. Author proves that the energy of perturbations tends to zero as \(t\to \infty\), providing that the viscosity is sufficiently large, the energy at initial time is bounded and Reynolds number is sufficiently small. Aim of this work is to solve a problem that \textit{J. Leray} emphasized in a paper published in Acta Math. 63, 193-248 (1934). The result seems to be also promising for developing some stable numerical methods for external problems for Navier-Stokes equations.
scientific article; zbMATH DE number 4029111
scientific article