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.