Long time existence results for solutions of water waves equations

Abstract : We present in this report various results obtained during the last years by several authors about the problem of long time existence of solutions of water waves and related equations with initial data that are small, smooth, and decaying at infinity. After recalling some facts about local existence theory, we focus mainly on global existence theorems for gravity waves equations proved by Ionescu-Pusateri, Alazard-Delort and Ifrim-Tataru. We describe some of the ideas of the proofs of these theorems, and conclude the paper mentioning related results.
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Communication dans un congrès
Boyan Sirakov, Paulo Ney de Souza, Marcelo Viana. International Congress of Mathematicians, Aug 2018, Rio de Janeiro, Brazil. World Scientific Publishing Co Pte Ltd, 3, pp.2259, 2018, Proceedings of the International Congress of Mathematicians, Rio de Janeiro, 2018
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Jean-Marc Delort. Long time existence results for solutions of water waves equations. Boyan Sirakov, Paulo Ney de Souza, Marcelo Viana. International Congress of Mathematicians, Aug 2018, Rio de Janeiro, Brazil. World Scientific Publishing Co Pte Ltd, 3, pp.2259, 2018, Proceedings of the International Congress of Mathematicians, Rio de Janeiro, 2018. 〈hal-01856416〉

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