The vanishing viscosity limit of statistical solutions of the Navier-Stokes equations. II. The general case

AbstractWe study problems of vanishing viscosity limit of statistical solutions of the Navier-Stokes equation in 3-D and general boundary conditions in 2-D. In this case due to lack of sufficiently strong estimate besides energy type one we can have only weak convergence in the limit. By a statistical extension of the generalized Young measure theorem of R. DiPerna and A. Majda we show that a weak limit is a measure valued solution of the Euler equation. As another corollary of the extended Young measure theorem we show that any statistical solution generates measure valued solutions in a canonical fashion