Singular kinetic equations and applications

Rongchan Zhu (AMSS, Beijing)

Nov 18. 2021, 10:15 — 11:15

In this talk we consider singular kinetic equations on $\mathbb{R}^{2d}$ by the paracontrolled distribution method introduced by Gubinelli, Imkeller and Perkowski. We first develop paracontrolled calculus  in the kinetic setting, and  use it to establish the global well-posedness for the linear  singular kinetic equations under the assumptions that the products of singular terms are well-defined. We also demonstrate how the required products can be defined in the case that singular term is a Gaussian random field by probabilistic calculation. Interestingly,  although the terms in the zeroth  Wiener chaos of regularization approximation are not zero, they converge in suitable weighted Besov spaces and no renormalization is required. As applications  the global well-posedness for a nonlinear kinetic equation with singular coefficients is obtained by the entropy method. Moreover, we also solve the martingale problem for nonlinear kinetic distribution dependent stochastic differential equations with singular drifts. This talk is based on the joint work with Zimo Hao, Xicheng Zhang and Xiangchan Zhu.

Further Information
ESI Boltzmann Lecture Hall
Slides Berglund
Associated Event:
Higher Structures Emerging from Renormalisation (Graduate School)
Pierre Clavier (U of Haut-Alsace)
Kurusch Ebrahimi-Fard (NTNU, Trondheim)
Peter K. Friz (TU Berlin)
Harald Grosse (U of Vienna)
Dominique Manchon (U Clerment Auvergne)
Sylvie Paycha (U of Potsdam)
Sylke Pfeiffer (U of Potsdam)