Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Global solutions for coupled Kuramoto-Sivashinsky-KdV system


Authors: Maomao Cai and Dening Li
Journal: Quart. Appl. Math. 67 (2009), 477-488
MSC (2000): Primary 35Q53, 35Q80; Secondary 76E99
DOI: https://doi.org/10.1090/S0033-569X-09-01148-8
Published electronically: May 6, 2009
MathSciNet review: 2547636
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Abstract: 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$.


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Additional Information

Maomao Cai
Affiliation: Department of Mathematics, West Virginia University, Morgantown, WV 26506, USA
Address at time of publication: (Maomao Cai) Department of Mathematics, Weber State University, Ogden, UT 84405, USA
Email: mcai@math.wvu.edu

Dening Li
Affiliation: Department of Mathematics, West Virginia University, Morgantown, WV 26506, USA
Email: li@math.wvu.edu

DOI: https://doi.org/10.1090/S0033-569X-09-01148-8
Keywords: Kuramoto-Sivashinsky-KdV system, global solution
Received by editor(s): February 17, 2008
Published electronically: May 6, 2009
Additional Notes: The first author was supported in part by DoDEPSCOR N000014-02-1-0577
The second author was supported in part by DoDEPSCOR N000014-02-1-0577 and WVU Faculty Development Fund
Article copyright: © Copyright 2009 Brown University
The copyright for this article reverts to public domain 28 years after publication.


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