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
Stochastic perturbations
Boltzmann equation
Tagged particle - distinguished particle
Brownian motion
76P05 - Rarefied gas flows, Boltzmann equation [See also 82B40, 82C40, 82D05]
74B15 - Equations linearized about a deformed state (small deformations superposed on large)
70Hxx - Hamiltonian and Lagrangian mechanics [See also 37Jxx]
37Kxx - Infinite-dimensional Hamiltonian systems [See also 35Axx, 35Qxx]
76-XX - Fluid mechanics {For general continuum mechanics, see 74Axx, or other parts of 74-XX}
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
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Bodineau- Notes
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Boudineau_Linearized
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14386
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14386.mp4
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