Special Session 10: Recent Developments in Regularity Theory for PDEs

The hydrodynamic limit of the discrete-velocity BGK Boltzmann equation
Zhongyang Gu
Shenzhen University
Peoples Rep of China
Co-Author(s):    Xin Hu, Tsuyoshi Yoneda
Abstract:
In this talk, we will present the construction of a global weak solution to the $3$-dimensional incompressible Navier-Stokes equations through the study of the hydrodynamic limit of the discrete-velocity BGK Boltzmann equation, provided the smallness of the initial data. In particular, the derivation of the diffusion term from the microstructure will be explained. This talk is based on a joint work with Xin Hu (Wuhan University) and Tsuyoshi Yoneda (Hitotsubashi University).