Stable invariant manifolds for coupled Navier–Stokes and second-order wave systems

Abstract

This article considers the dynamics of a coupled system of incompressible Navier–Stokes equations with second-order wave equations. The system may be used to approximate the interaction of ionized plasma particles with an electromagnetic field. Under appropriate assumptions and provided that the viscosity is sufficiently large, we prove the existence of an invariant manifold. Moreover, the manifold is attractive as t→+∞ for all close neighboring solutions.