## Duke Mathematical Journal

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

#### Article information

Source
Duke Math. J. Volume 71, Number 1 (1993), 1-21.

Dates
First available in Project Euclid: 20 February 2004

Permanent link to this document
http://projecteuclid.org/euclid.dmj/1077289834

Digital Object Identifier
doi:10.1215/S0012-7094-93-07101-3

Mathematical Reviews number (MathSciNet)
MR1230283

Zentralblatt MATH identifier
0787.35090

Subjects
Primary: 35Q53: KdV-like equations (Korteweg-de Vries) [See also 37K10]

#### Citation

Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis. The Cauchy problem for the Korteweg-de Vries equation in Sobolev spaces of negative indices. Duke Math. J. 71 (1993), no. 1, 1--21. doi:10.1215/S0012-7094-93-07101-3. http://projecteuclid.org/euclid.dmj/1077289834.

#### References

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• [2] J. Bourgain, Korteweg-de Vries with $L^2$ data, preprint.
• [3] J. Ginibre and Y. Tsutsumi, Uniqueness of solutions for the generalized Korteweg-de Vries equation, SIAM J. Math. Anal. 20 (1989), no. 6, 1388–1425.
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• [6] C. E. Kenig, G. Ponce, and L. Vega, Oscillatory integrals and regularity of dispersive equations, Indiana Univ. Math. J. 40 (1991), no. 1, 33–69.
• [7] C. E. Kenig, G. Ponce, and L. Vega, Well-posedness of the initial value problem for the Korteweg-de Vries equation, J. Amer. Math. Soc. 4 (1991), no. 2, 323–347.
• [8] C. E. Kenig, G. Ponce, and L. Vega, Well-posedness and scattering results for the generalized Korteweg-de Vries equation via contraction principle, to appear in Comm. Pure Appl. Math.
• [9] S. N. Kruzhkov and A. V. Faminskiĭ, Generalized solutions of the Cauchy problem for the Korteweg-de Vries equation, Math. USSR-Sb. 48 (1984), 93–138.
• [10] R. S. Strichartz, Restrictions of Fourier transforms to quadratic surfaces and decay of solutions of wave equations, Duke Math. J. 44 (1977), no. 3, 705–714.
• [11] Y. Tsutsumi, The Cauchy problem for the Korteweg-de Vries equation with measures as initial data, SIAM J. Math. Anal. 20 (1989), no. 3, 582–588.