Well-posedness and persistence property for the fifth-order Fokas-Olver-Rosenau-Qiao equation

In this paper, we delve into an analysis of the fifth-order Fokas-Olver-Rosenau-Qiao (FORQ) equation. We demonstrate local well-posedness for this equation under the condition that an initial data \(u_0\in H^s(\mathbb {R})\) $u_0\in H^s(\mathbb{R})$ for some \(s>7/2\) $s>7/2$ . We examine global existence and blow-up scenario. Additionally, we study the persistence properties of the equation in weighted Sobolev spaces.