| Abstract: |
| We discuss a proof for the uniqueness and regularity of the invariant measure 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, can nevertheless be applied in this weakly dissipative setting to obtain unique ergodicity, albeit without mixing rates. Under the assumption of large damping, however, exponential mixing can be recovered. Time permitting, application of this approach to other weakly dissipative systems, such as the damped-driven Nonlinear Schrodinger equation, will also be discussed. |
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