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Results of Fractional Rough Burgers equation in $H^s$ space and its application
Shuolin Zhang, Zhaonan Luo, Zhaoyang Yin · 2025-11-28 · via math.PR updates on arXiv.org

In this paper, we study the well-posedness of Fractional Rough Burgers equation driven by space-time noise in $H^s(\mathbb T)$ space. For the higher dissipation $γ\in(\frac{4}{3},2]$, we establish local well-posedness. Global well-posedness is further obtained when $γ$ is restricted to the interval $(\frac{5}{3}, 2]$. For the lower dissipation $γ\in(\frac{5}{4},\frac{4}{3}]$, we use the regularity analysis derivation the para-controlled solution.

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