A Priori Estimates for Singular Fractional Stochastic Burgers Equations

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.