The vanishing viscosity limit of statistical solutions of the Navier- Stokes equations. I: 2-D periodic case
The author studies the family of statistical solutions \(P^{\epsilon}_ t\) (with a common initial data \(P_ 0)\) of the Navier-Stokes equations \(u_ t+(\nabla \cdot u)u+\nabla p=\epsilon \Delta u\), \(\nabla \cdot u=0\) in the 2-dimensional periodic domain with a small viscosity \(\epsilon\). The main result is the strong compactness of the family \(\{P^{\epsilon}_ t|\epsilon \in (0,1]\}\). Thus by choosing a subsequence the author obtains a global in time statistical solution of the Euler equations. The uniqueness remains open. [For part II see the following review.]
scientific article; zbMATH DE number 4210680
scientific article