Asymptotic stability of three-dimensional incompressible inhomogeneous Navier-Stokes equations driven by gravity

We study the asymptotic stability of hydrostatic equilibrium to incompressible inhomogeneous Navier-Stokes equations driven by gravity under non-slip boundary conditions in a strip domain R 2 × ( 0 , 1 ) . If hydrostatic density increases strictly along the direction of gravity, the global existence of solutions to perturbated equations is shown as well as explicit decay rates of solutions. This reflects the well-known Rayleigh-Taylor stability phenomenon.