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

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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.

Topics & Keywords

Advanced Mathematical Physics Problems Nonlinear Waves and Solitons Mathematical Analysis and Transform Methods

UN Sustainable Development Goals

Reduced inequalities

Publication Details

Published in: SIAM Journal on Mathematical Analysis

Volume 33, Issue 4, pp. 982-988

DOI: 10.1137/s0036141001385307

Field-Weighted Citation Impact: 9.94

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