Dynamical Systems and Partial Differential Equations seminars
These are the research seminars of the Dynamical systems and Partial Differential Equations group.
Seminar details
Day and time: Tuesdays from 2pm - 3pm or Friday's from 2pm - 3pm
Venue: 39 AA 04
Open to: Staff and students.
For further information, please contact the organisers Jon Bevan and Sergey Zelik.
Upcoming seminars
On the unique ergodicity, regularity, and mixing for the weakly-damped stochastic KdV equation
Speaker: Vincent Martinez (http://math.hunter.cuny.edu/vmartine/)
Date: Friday 16 September, 2-3pm
Venue: 39AA04
Abstract: We discuss the existence, uniqueness, and regularity of invariant measures for the damped-driven stochastically forced 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, a one-force, one-solution principle is established, from which we are able to deduce the existence of a spectral gap with respect to a Wasserstein distance-like function. Our treatment is paradigmatic and should be applicable to many other weakly dissipative systems that are stochastically forced in this way.