Ill-Posedness Issues for the Benjamin--Ono and Related Equations

L. Molinet, J. C. Saut, N. Tzvetkov

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Source: Crossref

Published: Jan 1, 2001

DOI: 10.1137/s0036141001385307

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Source abstract

We establish that the Cauchy problem for the Benjamin--Ono equation and for a rather general class of nonlinear dispersive equations with dispersion slightly weaker than that of the Korteweg--de Vries equation cannot be solved by an iteration scheme based on the Duhamel formula. As a consequence, the flow map fails to be smooth.

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