Séminaire d'Analyse
Unconditional uniqueness for periodic nonlinear dispersive equationsNobu Kishimoto
Thursday 17 March 2016 10:45 - Tours - Salle 1180 (Bât E2)
Résumé :
When a solution to the Cauchy problem for a nonlinear evolution equation is obtained by a fixed point argument using auxiliary function spaces, uniqueness of solutions in a natural space (e.g., space of continuous functions with values in the same Banach space as initial data), which we call unconditional uniqueness, becomes a non-trivial property, and to show that often requires some additional work. Recently, unconditional uniqueness for some nonlinear dispersive equations (such as the Korteweg-de Vries equation and nonlinear Schrodinger equations) in the periodic setting has been shown by a simple integration by parts argument, which can be regarded as a variant of the normal form reduction. In this talk, we review some results in this direction and introduce an abstract framework, which is applicable to a wide variety of nonlinear dispersive equations.
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