On the well-posedness of the hydrostatic limit in fluid mechanics

English

Séminaire Modèles et Algorithmes Déterministes: EDP-MOISE

29/05/2012 - 15:00 Mr Michael Renardy (Virginia Tech) Salle 1 - Tour IRMA

The talk will review some recent results on the well-posedness of hydrostatic Euler equations. In particular, the role of boundary conditions (walls or free surface) will be emphasized. The results show that well-posedness of these equations is not a local property, for  instance, it turns out that flows with one free surface are well-posed while flows with two free  surfaces
are ill-posed. It is also shown that magnetic fields or fluid elasticity can restore the  well-posedness of the equations. I shall also discuss the implications for boundary layers in high Weissenberg number viscoelastic flows.