Well-Posedness and Time Regularity for a System of Modified Korteweg-de Vries-Type Equations in Analytic Gevrey Spaces

Abstract

Studies of modified Korteweg-de Vries-type equations are of considerable mathematical interest due to the importance of their applications in various branches of mechanics and physics. In this article, using trilinear estimate in Bourgain spaces, we show the local well-posedness of the initial value problem associated with a coupled system consisting of modified Korteweg-de Vries equations for given data. Furthermore, we prove that the unique solution belongs to Gevrey space G σ × G σ in x and G 3 σ × G 3 σ in t. This article is a continuation of recent studies reflected.