Luigi C. Berselli and Stefano Spirito
A remark on the Euler equations in dimension two
Received: 8 October 2010
Accepted in revised form: 13 June 2011
Mathematics Subject Classification (2000): 35Q30, 76F65, 76D03, 76D09.
Keywords:2D Euler equations, Navier-Stokes equations, existence, singular limits.
Abstract: We review some results concerning the global existence of weak solutions to the Euler equations in a two dimensional open bounded set. These results are obtained by means of a suitable vanishing viscosity approximation, through the Navier-Stokes equations equipped with Navier-type boundary conditions. Next, we prove a theorem of existence for weak solutions with a given non-zero normal velocity, slightly relaxing with respect to the time variable the known assumptions on the data of the problem.