Well-posedness of short time solutions and non-uniform dependence on the initial data for a shallow water wave model in critical Besov space.

A nonlinear shallow water wave equation containing the famous Degasperis-Procesi and Fornberg-Whitham equations is investigated. The well-posedness of short time solutions is established to illustrate that the solution map of the equation is continuous in the critical Besov space B ∞ , 1 1 (R) . Using the methods to construct high and low frequency functions, we prove that the solution map of the equation is non-uniform continuous dependence on the initial data in B ∞ , 1 1 (R) . [ABSTRACT FROM AUTHOR]