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Remarks on the Korteweg-de Vries equation. (English) Zbl 0334.35062

MSC:
35Q99PDE of mathematical physics and other areas
35G25Initial value problems for nonlinear higher-order PDE
35B20Perturbations (PDE)
35D05Existence of generalized solutions of PDE (MSC2000)
35B45A priori estimates for solutions of PDE
References:
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[2]T. B. Benjamin,Lectures on Non-Linear Wave Motion: Lectures in Applied Mathematics, No. 15, Amer. Math. Soc., 1974.
[3]J. Bona, R. Scott,Solutions of the K. d. V. equation in fractional order Sobolev spaces, Duke Math. J. (to appear).
[4]J. Bona, R. S. Smith,The initial value problem for the Korteweg-de Vries equation, Philos. Trans. Roy. Soc. London278 (1975), 555–604. · Zbl 0306.35027 · doi:10.1098/rsta.1975.0035
[5]Dushane,Generalizations of the Korteweg-de Vries equation, Proc. Symp. in Pure Math.23 (1971).
[6]T. Kato,Quasilinear equations of evolution, with applications to partial differential equations, inSpectral theory and differential equations: Lecture Notes in Mathematics, Vol. 448, Springer-Verlag, 1974.
[7]T. Kato,The Cauchy problem for quasilinear symmetric hyperbolic equations (to appear).
[8]P. D. Lax,Periodic solutions of the K. d. V. equations, Comm. Pure Appl. Math.28 (1975), 141–188. · Zbl 0302.35008 · doi:10.1002/cpa.3160280105
[9]J. C. Saut,Applications de l’interpolation non linéaire à des problèmes d’évolution non linéaires, J. Math. Pures Appl.9 (Sér. 54) (1974), 27–52.
[10]J. C. Saut,Sur certaines généralisations de l’équation de Korteweg-de Vries, C. R. Acad. Sc. Paris280 (1975), 653–656.
[11]W. A. Strauss,On the regularity of functions with values in various Banach spaces, Pacific J. Math.19 (1966), 543–551.
[12]L. Tartar,Interpolation non linéaire et régularité, J. Functional Analysis9 (1972), 469–489. · Zbl 0241.46035 · doi:10.1016/0022-1236(72)90022-5
[13]R. Temam,Sur un problème non linéaire, J. Math. Pures Appl.48 (1969), 159–172.
[14]R. Temam,Proceedings on a Conference on Mathematical Problems in Turbulence: Lecture Notes in Mathematics, Springer-Verlag (to appear).
[15]M. Tsutsumi, T. Mukasa,Parabolic regularizations for the generalized Korteweg-de Vries equation, Funkcial. Ekvac.14 (1971), 89–110.