The Navier-Stokes limit of the Boltzmann equation for bounded collision kernels
The Navier-Stokes limit for the Boltzmann equation with bounded collision kernels is discussed in complete detail. It is shown that the fluctuations of appropriately scaled sequences of renormalized solution of the Boltzmann equation (in the DiPerna-Lions sense) have as limit points weak Leray solutions of incompressible Navier-Stokes system. Assumptions on the sequences of renormalized solutions made in earlier papers devoted to the same problem are avoided in this work, so this paper completes the fluid dynamic limit theory for weak solutions at least for bounded collision kernels.
scientific article; zbMATH DE number 2078251
scientific article