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Global solutions for coupled Kuramoto-Sivashinsky-KdV system. (English) Zbl 1169.35371
Summary: We study the global smooth solution for the coupled Kuramoto-Sivanshinsky-KdV system in two-dimensional space. The model is proposed to describe the surface waves on multi-layered liquid films. The global solution is obtained for general initial data, using an a priori estimate for the nonlinear system, and the smoothness of such solution is established in $ t >0$.

35Q53KdV-like (Korteweg-de Vries) equations
35Q80Applications of PDE in areas other than physics (MSC2000)
76E99Hydrodynamic stability
35B35Stability of solutions of PDE
35B45A priori estimates for solutions of PDE
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