Global attractor for the periodic generalized Korteweg-De Vries equation through smoothing

<p style='text-indent:20px;'>We establish a smoothing result for the generalized KdV (gKdV) on torus with polynomial non-linearity, damping, and forcing that matches level gKdV at <inline-formula><tex-math id="M1">\begin{document}$ H^1 $\end{document}</tex-math></inline-formula>. As consequence, we existence of global attractor this equation as well its compactness in id="M2">\begin{document}$ H^s(\mathbb{T}) $\end{document}</tex-math></inline-formula>, id="M3">\begin{document}$ s\in (1, 2). $\end{document}</tex-math></inline-formula></p>