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 $H^s(\m T)$ 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 $(\frac{3}{2}, 2]$. For the lower dissipation $γ\in(\frac{5}{4},\frac{4}{3}]$, we use the regularity analysis derivation the para-controlled solution.

💡 Research Summary

This paper investigates the well‑posedness of the Fractional Rough Burgers (FRB) equation driven by space‑time white noise in the Sobolev space (H^{s}(\mathbb T)). The equation under study is

\