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Instability results for super-critical nonlinear wave and Schrodinger equations
Slim Ibrahim
ASU
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Instability results for super-critical nonlinear wave and Schrodinger equations Slim Ibrahim ASU |
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ABSTRACT Nonlinear Schrodinger evolutions involve a dynamical balance between linear dispersive spreading of the wave and nonlinear self-interaction of the wave. In sub-critical settings, the dispersive spreading is stronger and therefore solutions are expected to exist globally in time. We show, that in supercritical case, the nonlinear self-interaction of the wave is much stronger. This leads to some sort of instability of the waves. |