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15 February 2001 On the ill-posedness of some canonical dispersive equations
Carlos E. Kenig, Gustavo Ponce, Luis Vega
Duke Math. J. 106(3): 617-633 (15 February 2001). DOI: 10.1215/S0012-7094-01-10638-8

Abstract

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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Carlos E. Kenig. Gustavo Ponce. Luis Vega. "On the ill-posedness of some canonical dispersive equations." Duke Math. J. 106 (3) 617 - 633, 15 February 2001. https://doi.org/10.1215/S0012-7094-01-10638-8

Information

Published: 15 February 2001
First available in Project Euclid: 13 August 2004

zbMATH: 1034.35145
MathSciNet: MR1813239
Digital Object Identifier: 10.1215/S0012-7094-01-10638-8

Subjects:
Primary: 35R25
Secondary: 35B30, 35B65, 35Q51, 35Q53

Rights: Copyright © 2001 Duke University Press

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Vol.106 • No. 3 • 15 February 2001
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