A Spectral Criterion for Stability of a Steady Viscous Incompressible Flow Past an Obstacle

We show that the question of stability of a steady incompressible Navier-Stokes flow V in a 3D exterior domain Ω is essentially a finite-dimensional problem (Theorem 3.2). Although the associated linearized operator has an essential spectrum touching the imaginary axis, we show that certain assumptions on the eigenvalues of this operator guarantee the stability of flow V (Theorem 4.1). No assumption on the smallness of the steady flow V is required.