Note on the stability of planar stationary flows in an exterior domain without symmetry

Abstract

The asymptotic stability of two-dimensional stationary flows in a non-symmetric exterior domain is considered. Under the smallness condition on initial perturbations, we show the stability of the small stationary flow whose leading profile at spatial infinity is given by the rotating flow decaying in the scale-critical order $O(|x{|}^{-1})$. Especially, we prove the $L^p$-$L^q$ estimates to the semigroup associated with the linearized equations.

arXiv comment49 pages, final version. To appear in Adv. Differential Equations

References in corpus (4)

• On the asymptotic stability of steady flows with nonzero flux in two-dimensional exterior domains
• On stationary Navier-Stokes flows around a rotating obstacle in two-dimensions
• Asymptotic structure of steady Stokes flow around a rotating obstacle in two dimensions
• On the existence of D-solutions of the steady-state Navier-Stokes equations in plane exterior domains