The local well-posedness, existence and uniqueness of weak solutions for a model equation for shallow water waves of moderate amplitude

摘要

This paper deals with the Cauchy problem for a nonlinear equation modeling the evolution of the free surface for waves of moderate amplitude in the shallow water regime, which was proposed by Constantin and Lannes (2009) [20]. Applying the pseudoparabolic regularization technique, the local well-posedness of strong solutions in Sobolev space H-s (R) with s > 3/2 is established via a limiting procedure. Moreover, a sufficient condition for the existence of weak solutions of the equation in lower order Sobolev space H-s (R) with 1 < s <= 3/2 is obtained. (C) 2015 Published by Elsevier Inc.