Remarks about the inviscid limit of the Navier - Stokes system

In this paper we prove two results about the inviscid limit of the NavierStokes system. The first one concerns the convergence in H of a sequence of solutions to the Navier-Stokes system when the viscosity goes to zero and the initial data is inH. The second result deals with the best rate of convergence for vortex patch initial data in 2 and 3 dimensions. We present here a simple proof which also works in the 3D case. The 3D case is new. 1 The inviscid limit The Navier-Stokes system is the basic mathematical model for viscous incompressible flows. In a bounded domain, it reads  ∂tu+ u.∇u− ν∆u+∇p = 0, div(u) = 0, u = 0 on ∂Ω, (1) where u is the velocity, p is the pressure and ν is the kinematic viscosity. We can define a typical length scale L and a typical velocity U . The dimensionless ∗Courant Institute, New York University 251 Mercer St, New York, NY 10012