Well-posedness of the initial value problem for the Korteweg-de Vries equation

Kenig, Carlos E. ; Ponce, Gustavo ; Vega, Luis

Journal of the American Mathematical Society, Tome 04 (1991) no. 2, pp. 323-347

Détail

DOI : 10.1090/S0894-0347-1991-1086966-0

Bibliographie

[1] Bona, Jerry, Scott, Ridgway Solutions of the Korteweg-de Vries equation in fractional order Sobolev spaces Duke Math. J. 1976 87 99

[2] Bona, J. L., Smith, R. The initial-value problem for the Korteweg-de Vries equation Philos. Trans. Roy. Soc. London Ser. A 1975 555 601

[3] Calderã³N, A.-P. Commutators of singular integral operators Proc. Nat. Acad. Sci. U.S.A. 1965 1092 1099

[4] Carleson, Lennart Some analytic problems related to statistical mechanics 1980 5 45

[5] Coifman, R. R., Meyer, Yves Nonlinear harmonic analysis, operator theory and P.D.E 1986 3 45

[6] Constantin, P., Saut, J.-C. Local smoothing properties of dispersive equations J. Amer. Math. Soc. 1988 413 439

[7] Dahlberg, Bjã¶Rn E. J., Kenig, Carlos E. A note on the almost everywhere behavior of solutions to the Schrödinger equation 1982 205 209

[8] Ginibre, J., Velo, G. Scattering theory in the energy space for a class of nonlinear Schrödinger equations J. Math. Pures Appl. (9) 1985 363 401

[9] Ginibre, J., Velo, G. Commutator expansions and smoothing properties of generalized Benjamin-Ono equations Ann. Inst. H. Poincaré Phys. Théor. 1989 221 229

[10] Ginibre, J., Tsutsumi, Y. Uniqueness of solutions for the generalized Korteweg-de Vries equation SIAM J. Math. Anal. 1989 1388 1425

[11] Kato, Tosio On the Cauchy problem for the (generalized) Korteweg-de Vries equation 1983 93 128

[12] Kato, Tosio, Ponce, Gustavo Commutator estimates and the Euler and Navier-Stokes equations Comm. Pure Appl. Math. 1988 891 907

[13] Kenig, Carlos E., Ponce, Gustavo, Vega, Luis On the (generalized) Korteweg-de Vries equation Duke Math. J. 1989 585 610

[14] Kenig, Carlos E., Ponce, Gustavo, Vega, Luis Oscillatory integrals and regularity of dispersive equations Indiana Univ. Math. J. 1991 33 69

[15] Kenig, Carlos E., Ruiz, Alberto A strong type (2,2) estimate for a maximal operator associated to the Schrödinger equation Trans. Amer. Math. Soc. 1983 239 246

[16] Kruzhkov, S. N., Faminskiä­, A. V. Generalized solutions of the Cauchy problem for the Korteweg-de Vries equation Mat. Sb. (N.S.) 1983 396 425

[17] Marshall, Bernard Mixed norm estimates for the Klein-Gordon equation 1983 638 649

[18] Miura, Robert M. The Korteweg-de Vries equation: a survey of results SIAM Rev. 1976 412 459

[19] Ono, Hiroaki Algebraic solitary waves in stratified fluids J. Phys. Soc. Japan 1975 1082 1091

[20] Pecher, Hartmut Nonlinear small data scattering for the wave and Klein-Gordon equation Math. Z. 1984 261 270

[21] Ponce, Gustavo On the global well-posedness of the Benjamin-Ono equation Differential Integral Equations 1991 527 542

[22] Ponce, Gustavo, Vega, Luis Nonlinear small data scattering for the generalized Korteweg-de Vries equation J. Funct. Anal. 1990 445 457

[23] Saut, J.-C. Sur quelques généralisations de l’équation de Korteweg-de Vries J. Math. Pures Appl. (9) 1979 21 61

[24] Saut, J. C., Temam, R. Remarks on the Korteweg-de Vries equation Israel J. Math. 1976 78 87

[25] Stein, E. M. Oscillatory integrals in Fourier analysis 1986 307 355

[26] Stein, Elias M., Shakarchi, Rami Fourier analysis 2003

[27] Strichartz, Robert S. Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations Duke Math. J. 1977 705 714

[28] Tomas, Peter A. A restriction theorem for the Fourier transform Bull. Amer. Math. Soc. 1975 477 478

[29] Vega, Luis Schrödinger equations: pointwise convergence to the initial data Proc. Amer. Math. Soc. 1988 874 878