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A Priori Estimates for Singular Fractional Stochastic Burgers Equations
Abstract
We study the periodic fractional stochastic Burgers equation (∂t+Λγ)u=∂x(u2)+|∂x|1−αξ, where 1<γ≤ 2 and ξ is space-time white noise. Under the condition α>max(7−4γ)/2,(15−8γ)/6, we establish pathwise L1, 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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BibTeX
@misc{ji2026priori,
title = {{A Priori Estimates for Singular Fractional Stochastic Burgers Equations}},
author = {Xiaohao Ji},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2608.29726},
eprint = {2608.29726},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.29726},
}
RIS
TY - UNPB
TI - A Priori Estimates for Singular Fractional Stochastic Burgers Equations
AU - Xiaohao Ji
PY - 2026
DA - 2026/08/30
PB - arXiv
DO - 10.48550/arxiv.2608.29726
UR - https://arxiv.org/abs/2608.29726
AB - We study the periodic fractional stochastic Burgers equation (∂_t+Λ^γ)u=∂_x(u^2)+|∂_x|^1−αξ, where 1<γ≤ 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.
ER -