From particles to linear hydrodynamic equations
New challenges in PDE: Deterministic dynamics and randomness in high and infinite dimensional systems October 19, 2015 - October 30, 2015
Location: MSRI: Simons Auditorium
Ideal gas - particles as hard spheres
Infinite particle limit
Low density limit
Fast relaxation limit
Fluid equations - hydrodynamics
Tagged particle - distinguished particle
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
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