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
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
35L03 - Initial value problems for first-order 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]
14386
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
Bodineau- Notes
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Boudineau_Linearized
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14386
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14386.mp4
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