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We consider the Euler équation for incompressible fluids in a two dimensional domain depending on the time. In this situation we prove the existence of a weak solution and the existence ..œuLuniqueiLess jof_a smooth solution when the size of the domain increases fast enough with the time. Résumé. — On considère Véquation d* Euler dans un domaine à deux dimensions variant avec le temps. Dans cette situation nous prouvons Vexistence d'une solution faible et Vexistence et Vunicité d'une solution forte quand la taille du domaine augmente avec le temps.

On the existence and the regularity of an initial boundary problem of vorticity equation