Local Well-posedness of a Nutku-Oguz-Burgers System With Time Dependent Coefficients

Abstract

In this paper we study the local well-posedness of the initial value problem for a Nutku-Oguz-Burgers system with time dependent coefficients, formed by two Korteweg-de Vries equations coupled through the non-linear terms. The system appears as a model of wave propagation in a shallow channel with variable bottom surface, in which both nonlinear and dispersive effects are relevant. The proof of existence and uniqueness of local solution and the continuous dependence on the initial data of the local solution in Sobolev spaces Hs(R)xHs(R), s > 3/2, are based on the works [9] and [17]

Keywords

• Initial alue problem
• Korteweg-de Vries equations
• Local well-posedness
• Sobolev Spaces