Lower regularity solutions of a class of non-homogeneous boundary value problems of the Korteweg-de Vries equation on a finite domain

Abstract

In this paper, we study an initial-boundary value problem of the Korteweg-de Vries equation posed on a bounded interval $(0,L)$ with nonhomogeneous boundary conditions, which is known to be locally well-posed in the Sobolev space $H^s(0,L)$ with $s\gt-3/4$. Taking the advantage of the hidden dissipative mechanism and the sharp trace regularities of its solutions, we show that the problem is locally well-posed in the space $H^s(0,L)$ with $s\gt-1$.