Stochastic nonlinear dispersive equations: SNLB and SNLS

2018/02/09 Fri 16:45 - 17:45
Razvan Mosincat
The University of Edinburgh

We consider the stochastic nonlinear beam equations (SNLB) with additive space-time white noise forcing posed on the three-dimensional torus. By studying the regularity property of the stochastic forcing term, we prove local-in-time well-posedness (existence, uniqueness and stability of solutions) for all power-type nonlinearities. Moreover, in the defocusing case, we also prove global-in-time well posedness when the degree of the nonlinearity is sufficiently small. This is joint work with Oana Pocovnicu (Heriot-Watt University, UK), Leonardo Tolomeo (University of Edinburgh, UK), and Yuzhao Wang (University of Birmingham, UK).  We also study the well-posedness of stochastic nonlinear Schrödinger equations (SNLS) on $d$-dimensional tori with either additive or multiplicative stochastic forcing, the noise being white in time but smoother in space. This second part is joint work with Kelvin Cheung (Heriot-Watt University, UK).