报告题目：Variance blowup phenomena for the nonlinear wave equation with random initial data

报 告 人：刘劭 博士后（北京理工大学）

报告时间：2026年10月29日（星期四）14：00—15：00

报告地点：数学科学学院114（小报告厅）          

校内联系人： 程梦雨 副教授 联系方式：84708351-8206

报告摘要：In this talk, we study the two-dimensional quadratic nonlinear wave equation (NLW) with Gaussian initial data in the regime where one of the stochastic objects arising in the construction of solutions has infinite variance. This regime occurs before the critical regularity predicted by the probabilistic scaling heuristics of Deng–Nahmod–Yue (2023). Consequently, standard probabilistic methods for constructing solutions fail.

Our main result shows that, for suitably renormalized, frequency-truncated Gaussian initial data, the corresponding solutions to the NLW converge locally in time to solutions of a stochastic NLW with zero initial data.

In particular, an interesting phenomenon emerges: the randomness propagates from the initial condition to the equation itself, giving rise to an effective time-correlated space-time Gaussian noise whose covariance exhibits a Bessel-type structure. Our proof combines paracontrolled calculus, the fourth moment method, and multilinear dispersive smoothing.

This talk is based on joint work with Guopeng Li (BIT), Jiawei Li (University of Edinburgh), Tadahiro Oh (University of Edinburgh / BIT), and Nikolay Tzvetkov (ENS Lyon).

报告人简介：刘劭，北京理工大学博士后，博士毕业于德国波恩大学，研究兴趣为非线性色散方程的确定性与概率性理论。