A Priori Estimates for Singular Fractional Stochastic Burgers Equations

Xiaohao Ji

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arXiv · 2608.29726

A Priori Estimates for Singular Fractional Stochastic Burgers Equations

Xiaohao Ji

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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.

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Xiaohao Ji. 2026-08-30. A Priori Estimates for Singular Fractional Stochastic Burgers Equations. https://arxiv.org/abs/2608.29726

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