From particles to linear hydrodynamic equations
Presenter
October 26, 2015
Keywords:
- Ideal gas, particles as hard spheres
- Infinite particle limit
- Low density limit
- Fast relaxation limit
- Fluid equations, hydrodynamics
- Stochastic perturbations
- Boltzmann equation
- Tagged particle, distinguished particle
- Brownian motion
MSC:
- 60J65
- 82C40
- 76P05
- 35R15
- 74B15
- 70Hxx
- 37Kxx
- 76-xx
Abstract
We consider a tagged particle in a diluted gas of hard spheres. Starting from the hamiltonian dynamics of particles in the Boltzmann-Grad limit, we will show that the tagged particle follows a Brownian motion after an appropriate rescaling. We use the linear Boltzmann equation as an intermediate level of description for one tagged particle in a gas close to global equilibrium.