3 problems

Let $\rho(x,t)$ be the entropy solution of the scalar conservation law with initial data $\xi$. The initial data is either a white noise derived from a spectrally positive Lévy pro…

Let $u$ denote the parabolic Anderson model with two-dimensional white noise, and let its moment at time $t$ be understood in the sense considered by Gu and Wu. Gu and Wu's moment…

Let $\rho_\alpha$ be the Gaussian measure associated with random Fourier-series initial data for the cubic nonlinear Schrödinger equation on $\mathbb{T}$, and let $\alpha=0$, so th…