Promotion Talk by Minh Binh Tran

Date: August 31, 2022

Time: 3:00PM - 4:00PM

Location: Bloc 302

Description: Title: On the wave turbulence theory for a stochastic KdV type equation
Abstract: In this talk, I will discuss our recent joint works with Gigliola Staffilani (MIT). In those papers, starting from the stochastic Zakharov-Kuznetsov (ZK) equation, a multidimensional KdV type equation, on a hypercubic lattice, we provide a rigorous derivation of both the homogeneous and inhomogeneous 3-wave kinetic equation. We show that the two point correlation function can be asymptotically expressed as the solution of the 3-wave kinetic equation at the kinetic limit under very general assumptions: the initial condition is out of equilibrium, the dimension is d ≥ 2, the smallness of the nonlinearity λ is allowed to be independent of the size of the lattice, the weak noise is chosen not to compete with the weak nonlinearity and not to inject energy into the equation. To the best of our knowledge, the work provides the first rigorous derivation of nonlinear 3-wave kinetic equations, for both homogeneous and inhomogeneous cases. Moreover, this is the first derivation for wave kinetic equations in the lattice setting and out-of-equilibrium.