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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 (11:00 AM PDT - 12:00 PM PDT)
Speaker(s): Isabelle Gallagher (École Normale Supérieure)
Location: SLMath: Eisenbud Auditorium
  • Boltzmann hierarchy

  • linearized Boltzmann

  • Ideal gas

  • particles as hard spheres

  • Infinite particle limit

  • Low density limit

  • Fluid equations

  • linear hydrodynamics

  • Tagged particle

  • distinguished particle

  • Brownian motion

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


We derive the linear acoustic and Stokes-Fourier equations as the limiting dynamics of a system of hard spheres in a diluted gas in two space dimensions. We assume the system is initially close to equilibrium and we use the linearized Boltzmann equation as an intermediate step.

Joint work with T. Bodineau, L. Saint-Raymond

24865?type=thumb Gallagher-Notes 237 KB application/pdf Download
Video/Audio Files


H.264 Video 14387.mp4 327 MB video/mp4 rtsp://videos.msri.org/data/000/024/643/original/14387.mp4 Download
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