Claude Bardos, Laboratoire J.-L. Lions, Paris,
"Boundary effects in the vanishing viscosity limit of solutions of Navier-Stokes equations with no slip boundary condition”
Abstract: In this talk, I consider the zero viscosity (
) limit of solutions of the 2d Navier-Stokes equations, subject to no-slip boundary condition, and will elaborate on two complementary problems:
• The convergence to the solution of the Euler equations under strong analyticity hypothesis during a short time interval 
to emphasize the role of the curvature of the boundary on this time 
of validity in connection with the size of Gortler vortices.
• To prove that the Onsager’s Hölder regularity exponent 
of the velocity field 
of a weak solution of the Euler equations implies the same regularity for the pressure. Then to use this remark to prove that in the zero viscosity limit of 
bounded solutions of the Navier-Stokes equations, in 
with 
, there is no anomalous energy dissipation.
These observations are part of a program initiated with E. Titi around 2007 and continuing with the contribution of other colleagues in particular presently Toan Nguyen, Trinh Nguyen and D. Boutros.