Stability of solution of Kuramoto-Sivashinsky-Korteweg-de Vries system

Abstract-A model consisting of a mixed Kuramoto-Sivashinsky-Korteweg-de Vries equation, linearly coupled to an extra linear dissipative equation has been proposed in [1] in order to describe the surface waves on multilayered liquid films and stability criteria are discussed using wave mode analysis. In this paper, we study the linear stability of solutions to the model from the viewpoint of energy estimate

Solutions for 2-dimensional stabilized Kuramoto -Sivashinsky system

We study a stabilized Kuramoto-Sivanshinsky system in two-dimensional space. A model consists of a mixed Kuramoto-Sivanshinsky-Korteweg-de Vires equation, linearly coupled to an extra linear dissipative equation. The model is proposed to describe the surface waves on multi-layered liquid films. In this work, we investigate the stability of the solution to this system by establishing a priori energy estimate for the linearized problem of this non-linear system. We use linear iteration to prove the local existence of the solution to this system. Based on a weak global priori energy estimate, we further prove the global existence and uniqueness of classical solution for this system