학술논문
Well-posedness of a highly nonlinear shallow water equation on the circle
Document Type
Working Paper
Source
Nonlinear Analysis 197 (2020) 111849
Subject
Language
Abstract
We present a comprehensive introduction and overview of a recently derived model equation for waves of large amplitude in the context of shallow water waves and provide a literature review of all the available studies on this equation. Furthermore, we establish a novel result concerning the local well-posedness of the corresponding Cauchy problem for space-periodic solutions with initial data from the Sobolev space $H^s$ on the circle for $s>3/2$.