The Cauchy problem for the Korteweg-de Vries equation in Sobolev spaces of negative indices

Duke Mathematical Journal - Tập 71 Số 1 - 1993
Carlos E. Kenig, Gustavo Ponce, Luis Vega

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[3] J. Ginibre and Y. Tsutsumi, <i>Uniqueness of solutions for the generalized Korteweg-de Vries equation</i>, SIAM J. Math. Anal. <b>20</b> (1989), no. 6, 1388–1425.

[1] J. Bourgain, <i>Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations</i>, preprint.

[2] J. Bourgain, <i>Korteweg-de Vries with $L^2$ data</i>, preprint.

[4] T. Kappeler, <i>Solutions to the Korteweg-de Vries equation with irregular initial profile</i>, Comm. Partial Differential Equations <b>11</b> (1986), no. 9, 927–945.

[5] T. Kato, <i>On the Cauchy problem for the (generalized) Korteweg-de Vries equation</i>, Studies in Applied Mathematics, Adv. Math. Suppl. Stud., vol. 8, Academic Press, New York, 1983, pp. 93–128.

[6] C. E. Kenig, G. Ponce, and L. Vega, <i>Oscillatory integrals and regularity of dispersive equations</i>, Indiana Univ. Math. J. <b>40</b> (1991), no. 1, 33–69.

[7] C. E. Kenig, G. Ponce, and L. Vega, <i>Well-posedness of the initial value problem for the Korteweg-de Vries equation</i>, J. Amer. Math. Soc. <b>4</b> (1991), no. 2, 323–347.

[8] C. E. Kenig, G. Ponce, and L. Vega, <i>Well-posedness and scattering results for the generalized Korteweg-de Vries equation via contraction principle</i>, to appear in Comm. Pure Appl. Math.

[9] S. N. Kruzhkov and A. V. Faminskiĭ, <i>Generalized solutions of the Cauchy problem for the Korteweg-de Vries equation</i>, Math. USSR-Sb. <b>48</b> (1984), 93–138.

[10] R. S. Strichartz, <i>Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations</i>, Duke Math. J. <b>44</b> (1977), no. 3, 705–714.

[11] Y. Tsutsumi, <i>The Cauchy problem for the Korteweg-de Vries equation with measures as initial data</i>, SIAM J. Math. Anal. <b>20</b> (1989), no. 3, 582–588.