Existence of invariant measures for the stochastic damped KdV equation

الأصل · EN

We address the long time behavior of solutions of the stochastic Korteweg-de Vries equation du + (∂³ₓ u +u∂ₓ u +λu)dt = f dt+ΦdWₜ on R where f is a deterministic force. We prove that the Feller property holds and establish the existence of an invariant measure. The tightness is established with the help of the asymptotic compactness, which is carried out using the Aldous criterion.