Incompressible Navier-Stokes-Fourier Limit from The Boltzmann Equation: Classical Solutions

Ning Jiang (1) , Chao-Jiang Xu (2) , Huijiang Zhao (3)

1 Mathematical Sciences Center [Tsinghua]
2 LMRS - Laboratoire de Mathématiques Raphaël Salem
3 School of Mathematics and Statistics [Wuhan]

The global classical solution to the incompressible Navier-Stokes-Fourier equation with small initial data in the whole space is constructed through a zero Knudsen number limit from the solutions to the Boltzmann equation with general collision kernels. The key point is the uniform estimate of the Sobolev norm on the global solutions to the Boltzmann equation.

Mots clés: Incompressible Navier-Stokes-Fourier equation; Boltzmann Equation

Domaines: Equations aux dérivées partielles [math.AP]

Ning Jiang, Chao-Jiang Xu, Huijiang Zhao. Incompressible Navier-Stokes-Fourier Limit from The Boltzmann Equation: Classical Solutions. 2014. ⟨hal-00936202⟩