The local strong solutions and global weak solutions for a nonlinear equation (Q370075)

Summary: The existence and uniqueness of local strong solutions for a nonlinear equation are investigated in the Sobolev space \(C([0, T); H^s(\mathbb{R})) \cap C^1([0, T); H^{s-1}(\mathbb{R}))\) provided that the initial value lies in \(H^s(\mathbb{R})\) with \(s > 3/2\). Meanwhile, we prove the existence of global weak solutions in \(L^\infty([0, \infty); L^2(\mathbb{R}))\) for the equation.