Year: 2026
Type: preprint
Abstract: We study the periodic fractional stochastic Burgers equation $(\partial_t+Λ^γ)u=\partial_x(u^2)+|\partial_x|^{1-α}ξ$, where $1<γ\leq 2$ and $ξ$ is space-time white noise. Under the condition $α>\max{(7-4γ)/2,(15-8γ)/6}$, we establish pathwise $L^1$, energy, and Besov estimates for a transformed remainder. The argument combines a response decomposition with a conservative Zvonkin transformation. For $1<γ<2$, this produces a compensated nonlocal diffusion operator whose coercivity is coupled to a cubic-increment estimate adapted from the modified Karman--Howarth--Monin argument.
Source: arXiv (Cornell University)
Author: Ji, Xiaohao
Institution: Freie Universität Berlin
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204958844