Local well-posedness and blow-up criterion to a nonlinear shallow water wave equation

Abstract

The initial data problem to a nonlinear shallow water wave equation in nonhomogeneous Besov space is discussed. Using the decomposition of Littlewood-Paley and the properties of nonhomogeneous Besov space, we establish the well-posedness of short time solutions for the equation in the Besov space. A blow-up criterion of solutions is also obtained.

Keywords

• shallow water wave equation
• local well-posedness
• blow-up criterion
• besov space