Ill-posedness issues for nonlinear dispersive equations
arXiv:math/0411455
Abstract
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).
Notes based on a course given at Hokkaido University in September 2004
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- Local ill-posedness of the 1D Zakharov system
- Global well-posedness in the Energy space for the Benjamin-Ono equation on the circle
- Local well-posedness for the quasi-linear Hamiltonian Schrödinger equation on tori
- Ill-posedness for the Burgers equation in Sobolev spaces
- Ill-Posedness of the Third Order NLS Equation with Raman Scattering Term