Results of Fractional Rough Burgers equation in $H^s$ space and its application

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 $\gamma\in(\frac{4}{3},2]$, we establish local well-posedness. Global well-posedness is further obtained when $\gamma$ is restricted to the interval $(\frac{5}{3}, 2]$. For the lower dissipation $\gamma\in(\frac{5}{4},\frac{4}{3}]$, we use the regularity analysis derivation the para-controlled solution.