Well-posedness and wave breaking for a shallow water wave model with large amplitude
The author considers a Cauthy problem of highly nonlinear shallow wave equations. He establishes the local well-posedness of the equation in Besov spaces by using the Littlewood-Paley decomposition and transport equation theory, also determines the precise blow-up mechanism for the strong solutions and investigates the asymptotic behaviors of the strong equations to this equation at infinity. The results here improve the corresponding work for this model in [\textit{R. Quirchmayr}, J. Evol. Equ. 16, No. 3, 539--567 (2016; Zbl 1360.35189)].
scientific article; zbMATH DE number 7189577
scientific article