The space time resonance method and global existence of small surface waves.

The space time resonance method and global existence of small surface waves.

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Jalal Shatah, Courant Institute for Mathematics, NYC
Fine Hall 110

We will present a new approach to proving global existence of small solutions to dispersive equations. This approach combines the well established methods of vector fields and normal forms and extend them to show global existence of small amplitude surface water waves. We will also show how many of the well known results of existence of small solutions of dispersive equations can be simply established by the space time resonance method.