Well-posedness and regularity for the Fractional Rough Burgers equation in Sobolev spaces with an application

Abstract

In this paper, we study the well-posedness of Fractional Rough Burgers equation driven by space-time white noise in $H^s$ 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 $(\frac{8}{5},2]$. For the lower dissipation $\gamma \in (\frac{5}{4},\frac{4}{3}]$, we establish the para-controlled solution in ${\mathcal{C}}^s\cap H^s$.