Mathematics Colloquium
Vincent Martinez
CUNY Hunter College
Title: On ergodicity of the damped-driven stochastically forced KdV equation
Date: Friday, March 03, 2023
Place and Time: LOV 101, 3:05-3:55 pm
Abstract.
We discuss the existence, uniqueness, and regularity of invariant measures for damped-driven, stochastically forced KdV 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. On the other hand, in the regime of large damping, we establish a one-force, one-solution principle, which ensures existence of a spectral gap with respect to a Wasserstein distance-like function.