Duke Mathematical Journal

On the ill-posedness of some canonical dispersive equations

Carlos E. Kenig, Gustavo Ponce, and Luis Vega

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We study the initial value problem (IVP) associated to some canonical dispersive equations. Our main concern is to establish the minimal regularity property required in the data which guarantees the local well-posedness of the problem. Measuring this regularity in the classical Sobolev spaces, we show ill-posedness results for Sobolev index above the value suggested by the scaling argument.

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Duke Math. J., Volume 106, Number 3 (2001), 617-633.

First available in Project Euclid: 13 August 2004

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Zentralblatt MATH identifier

Primary: 35R25: Improperly posed problems
Secondary: 35B30: Dependence of solutions on initial and boundary data, parameters [See also 37Cxx] 35B65: Smoothness and regularity of solutions 35Q51: Soliton-like equations [See also 37K40] 35Q53: KdV-like equations (Korteweg-de Vries) [See also 37K10]


Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis. On the ill-posedness of some canonical dispersive equations. Duke Math. J. 106 (2001), no. 3, 617--633. doi:10.1215/S0012-7094-01-10638-8. https://projecteuclid.org/euclid.dmj/1092403945

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