Abstract
We study the coupled Kuramoto-Sivashinsky-KdV equations describing the surface waves on multilayered liquid films. A priori energy estimates for linearized problem are derived and local existence of solutions for initial-value problem is established.
Highlights
We study the coupled Kuramoto-Sivashinsky-KdV equations describing the surface waves on multilayered liquid films
This paper studies a two-dimensional coupled KuramotoSivashinsky-Korteweg-de Vries equation
Which was first introduced in [3] and is often called the Benney equation. This equation finds various applications in plasma physics, hydrodynamics, and other fields [4, 5]. Another version of the Benney equation was proposed in [1] for a real wave field u (x, t), based on the Kuramoto-SivashinskyKorteweg-de Vries (KS-KdV) equation, which is linearly coupled to an additional linear dissipative equation for an extra real wave field V (x, t) that provides for the stabilization of the zero background solution
Summary
This paper studies a two-dimensional coupled KuramotoSivashinsky-Korteweg-de Vries equation. This equation finds various applications in plasma physics, hydrodynamics, and other fields [4, 5] Another version of the Benney equation was proposed in [1] for a real wave field u (x, t), based on the KS-KdV equation, which is linearly coupled to an additional linear dissipative equation for an extra real wave field V (x, t) that provides for the stabilization of the zero background solution. In. ISRN Mathematical Physics this paper, we will use the energy estimate approach to study such solution and establish its linear stability and the local existence of such solution for initial-value problems.
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