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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

October 26, 2015 (09:30 AM PDT - 10:30 AM PDT)
Speaker(s): Thierry Bodineau (École Polytechnique)
Location: SLMath: Eisenbud Auditorium
  • 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

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC



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

24863?type=thumb Bodineau- Notes 47.4 KB application/pdf Download
24864?type=thumb Boudineau_Linearized 6.8 MB application/pdf Download
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