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
Full-text PDF Free Access
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Additional Information
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 $t >0$.
References
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References
- D. J. Benney, Long waves on liquid films, J. Math. Phys. 45(1966), 150-155. MR 0201125 (34:1010)
- M. Cai, D. Li and C. Rattanakul, Stability and existence of solutions for 2-dimensional coupled Kuramoto-Sivashinsky-KdV system (preprint).
- C. I. Christov and M. G. Velarde, Dissipative solitons, Physica D, 86(1995), 323-347. MR 1353963 (96h:35178)
- C. Elphick, G. R. Ierlev, O. Regev and E. A. Spiegel, Interacting localized structures with Galilean invariance, Phys. Rev. A, 44(1991), 1110-1122.
- B. F. Feng, B. A. Malomed and T. Kawahara, Stable periodic waves in coupled Kuramoto-Sivashinsky-Korteweg-de Vries equations, J. Phys. Soc. Jpn. 71 (2002), 2700-2707.
- B. F. Feng, B. A. Malomed and T. Kawahara, Cylindrical solitary pulses in a two-dimensional stabilized Kuramoto-Sivashinsky system, Physica D, 3035 (2002), 1-12. MR 1963855 (2004b:35282)
- J. A. Gear and R. Grimshaw, Weak and strong interactions between internal solitary waves, Stud. Appl. Math. 70(1984), 235-258. MR 742590 (85i:76013)
- T. Kato, The Cauchy problem for quasilinear symmetric hyperbolic systems, Arch. Rat. Mech. Anal. 58(1975), 181-205. MR 0390516 (52:11341)
- B. A. Malomed, B. F. Feng and T. Kawahara, Stabilized Kuramoto-Sivashinsky system, Phys. Rev. E 64, 046304(2001).
- A. Matsumura and T. Nishida, The initial value problem for the equations of motion of viscous and heat-conductive gases, J. Math. Kyoto Univ. 20-1 (1980), 67-104. MR 564670 (81g:35108)
- M. Renardy and R. Rogers, An introduction to partial differential equations, Springer-Verlag, New York, 2004. MR 2028503 (2004j:35001)
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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
MR Author ID:
194475
Email:
li@math.wvu.edu
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.
