Unique ergodicity for the damped-driven stochastic KdV equation

Abstract: We discuss the existence, uniqueness, and regularity of invariant measures for the damped-driven stochastic Korteweg-de Vries equation, where the noise is additive and sufficiently non-degenerate. It is shown that a simple, but versatile control strategy, typically employed to establish exponential mixing for strongly dissipative systems such as the 2D Navier-Stokes equations, can nevertheless be applied in this weakly dissipative setting to establish elementary proofs of both unique ergodicity, albeit without mixing rates, as well as regularity of the support of the invariant measure. Under the assumption of large damping, however, we are able to deduce the existence of a spectral gap with respect to a Wasserstein distance-like function. This is joint work with Nathan Glatt-Holtz (Indiana University) and Geordie Richards (Guelph University).

mathematical physicsanalysis of PDEsclassical analysis and ODEsdynamical systemsoptimization and control

Audience: researchers in the topic

Potomac region PDE seminar

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