The cauchy problem for a shallow water type equation

Communications in Partial Differential Equations

Volumn 23, Issue 1-2, 1998, Pages 123-139

  Himonas, A Alexandrou ^a   Misiołek, Gerard ^a  

^a UNIVERSITY OF NOTRE DAME   (United States)

Author keywords

Cauchy problem; Fourier transform; Global existence; Local; Periodic

Indexed keywords

EID: 0001214956     PISSN: 03605302     EISSN: None     Source Type: Journal    
DOI: 10.1080/03605309808821340     Document Type: Article

References (6)

1. J. Bourgain, Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. Part 1: Schrodinger equation., GAFA 3 (1993).
2. J. Bourgain, Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. Part 2: KdV equation, GAFA 3 (1993).
3. J. Bourgain, On the Cauchy problem for periodic KdV type equations, Jour. Fourier Anal. Appl. (1995).
4. R. Camassa and D. Holm, An integrable shallow water equation with peaked solitons, Phys. Rev. Lett. 71 (1993).
5. Y. Fang and M. Grillakis, Existence and uniqueness for Boussinessq type equations on a circle, Comm. P.D.E. 21 (1996).
6. C. Kenig, G. Ponce and L. Vega, Higher order nonlinear dispersive equations, Proc. A.M.S. 122 (1994).