Abstract
We consider the Cauchy problem of a shallow water equation and its local wellposedness.
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Fokas, A. S., Fuchssteiner, B.: Symplectic structures, their Bäcklund transformation and hereditary symmetries. Phys. D., 4, 47–66 (1981–1982)
Camassa, R., Holm, D.: An integrable shallow water equation with peaked solitons. Phys. Rev. Letters, 17, 1661–1664 (1993)
Constantin, A., Escher, J.: Well–posedness, global existence, and blowup phenomena for a periodic quasilinear hyperbolic equation. Comm. Pure Appl. Math., 51, 475–504 (1998)
Constantin, A., Escher, J.: Global weak solutions for a shallow water equation. Indiana Univ. Math. J., 47, 1525–1545 (1998)
Constantin, A., Escher, J.: On the structure of a family of quasilinear equations arising in shallow water theory. Math. Ann., 312, 403–416 (1998)
Himonas, A. A., Misiolek, G.: The Cauchy problem for a shallow water type equation. Comm. PDE, 23(2), 123–139 (1998)
Bourgain, J.: Fourier restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations I, Schrödinger equations. GAFA, 3, 107–156 (1993)
Bourgain, J.: Fourier restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations II, The Periodic KdV Equation. GAFA, 3, 209–262 (1993)
Kenig, C. E., Ponce, G., Vega. L.: The Cauchy problem for the Korteweg–de Vries equation in Sobolev spaces of negative indices. Duke Math. J., 71, 1–21 (1993)
Kenig, C. E., Ponce, G., Vega. L.: A bilinear estimate with applications to the KdV equation. J. Amer. Math., 9(2), 573–603 (1996)
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Liu, X.F., Jin, Y.Y. The Cauchy Problem of a Shallow Water Equation. Acta Math Sinica 21, 393–408 (2005). https://doi.org/10.1007/s10114-004-0420-5
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DOI: https://doi.org/10.1007/s10114-004-0420-5