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: 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
76B07  Freesurface potential flows for incompressible inviscid fluids
35L03  Initial value problems for firstorder hyperbolic equations
76E20  Stability and instability of geophysical and astrophysical flows
65N75  Probabilistic methods, particle methods, etc. for boundary value problems involving PDEs
65F05  Direct numerical methods for linear systems and matrix inversion
37Gxx  Local and nonlocal bifurcation theory for dynamical systems [See also 34C23, 34K18]
14387
We derive the linear acoustic and StokesFourier 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. SaintRaymond
GallagherNotes

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