Ill-posedness issues for nonlinear dispersive equations

Details Ill-posedness issues for nonlinear dispersive equations Ill-posedness issues for nonlinear dispersive equations

2004-11-20

arxiv.org/abs/math/0411455v2

GAKUTO International Series Mathematical Sciences and Applications, Volume 27 September, 2006

Mathematics

Analysis of PDEs

Notes based on a course given at Hokkaido University in September 2004

Scientific paper

These notes are devoted to the notion of well-posedness of the Cauchy problem for nonlinear dispersive equations. We present recent methods for proving ill-posedness type results for dispersive PDE's. The common feature in the analysis is that the proof of such results requires the construction of high frequency approximate solutions on small time intervals (possibly depending on the frequency).

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