Recent advances in random data problems for nonlinear dispersive equations (I)
Prof. Yu Deng
2023-07-12 16:10-17:10
MCM110&Online
Speaker: Prof. Yu Deng (University of Southern California)Time: 16:10-17:10 July 12, 2023 (Wednesday)
Place: MCM110 & Online (Zoom ID: 3329836068 Password: mcm1234)
Title: Recent advances in random data problems for nonlinear dispersive equations (I)
Abstract: In this talk we summarize the recent advancements in the study of random data problems for nonlinear dispersive equations, in connection with Gibbs measures that naturally occur in quantum field theory and statistical physics. Our main results resolve two of the three remaining open problems in this field: the invariance of Phi_2^p measures under Schrodinger dynamics and of Phi_3^4 under wave dynamics.
The proofs are based on the methods of random averaging operators and random tensors, which are inspired by the previous works in the contexts of stochastic PDEs. These are joint works with Andrea R. Nahmod and Haitian Yue.
