On the model equations which describe nonlinear wave motions in a rotating fluid
HTML articles powered by AMS MathViewer
- by Jong Uhn Kim PDF
- Trans. Amer. Math. Soc. 287 (1985), 403-417 Request permission
Abstract:
This paper concerns mathematical aspects of the two model equations describing nonlinear wave motions in a rotating fluid. We establish local existence of solutions and show that singularities occur in a finite time under certain hypotheses. We also show that these equations admit nonconstant travelling wave solutions.References
- T. Brooke Benjamin, Lectures on nonlinear wave motion, Nonlinear wave motion (Proc. AMS-SIAM Summer Sem., Clarkson Coll. Tech., Potsdam, N.Y., 1972) Lectures in Appl. Math., Vol. 15, Amer. Math. Soc., Providence, R.I., 1974, pp. 3–47. MR 0359517
- T. B. Benjamin, J. L. Bona, and J. J. Mahony, Model equations for long waves in nonlinear dispersive systems, Philos. Trans. Roy. Soc. London Ser. A 272 (1972), no. 1220, 47–78. MR 427868, DOI 10.1098/rsta.1972.0032 J. L. Bona, On solitary waves and their role in the evolution of long waves, Applications of Nonlinear Analysis in the Physical Sciences (H. Amann, N. Bazley and K. Kirchgässner, ed.), Pitman, London, 1981, pp. 183-205.
- Michael G. Crandall and Paul H. Rabinowitz, Bifurcation from simple eigenvalues, J. Functional Analysis 8 (1971), 321–340. MR 0288640, DOI 10.1016/0022-1236(71)90015-2
- Jack K. Hale, Ordinary differential equations, Pure and Applied Mathematics, Vol. XXI, Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1969. MR 0419901
- Tosio Kato, Quasi-linear equations of evolution, with applications to partial differential equations, Spectral theory and differential equations (Proc. Sympos., Dundee, 1974; dedicated to Konrad Jörgens), Lecture Notes in Math., Vol. 448, Springer, Berlin, 1975, pp. 25–70. MR 0407477 —, On the Korteweg-de Vries equations, Manuscripta Math. 28 (1979), 89-99.
- Jong Uhn Kim, Solutions to the equations of one-dimensional viscoelasticity in BV, SIAM J. Math. Anal. 14 (1983), no. 4, 684–695. MR 704484, DOI 10.1137/0514052
- S. Leibovich, Weakly non-linear waves in rotating fluids, J. Fluid Mech. 42 (1970), 803–822. MR 273890, DOI 10.1017/S0022112070001611 R. L. Seliger, A note on the breaking waves, Proc. Roy. Soc. London Ser. A 303 (1968), 493-496.
- David Westreich, Bifurcation at eigenvalues of odd multiplicity, Proc. Amer. Math. Soc. 41 (1973), 609–614. MR 328707, DOI 10.1090/S0002-9939-1973-0328707-9
Additional Information
- © Copyright 1985 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 287 (1985), 403-417
- MSC: Primary 35Q20; Secondary 76U05
- DOI: https://doi.org/10.1090/S0002-9947-1985-0766227-0
- MathSciNet review: 766227