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Navier-Stokes

Date: 11/Sep/2010

I’m currently interested in microscopic derivations of macroscopic equations, e.g. Navier-Stokes, Euler, …

It’s related to the macroscopic models for complex systems arising from biology, economy etc. (Direct and inverse problems)

I’m collecting here interesting some references about the subjects.

It seems that the problem of deriving the N-S equation from a limit N \to \infty of N-particle Newton equation is extremely hard at this moment ! In order to simplify the problem, people studied lattice models, but for fluids which can move freely in space lattice models cannot be very realistic ?!

References:

Horng-Tzer Yau, Scaling limits of particle systems, incompressible Navier-Stokes equations, and Boltzmann equation, Doc. Math. J. DMV, ICM 1998, III, 193-202 (and references therein): but why do particles have to collide ?!

Esposito, Lebowitz, Marra, On the derivation of hydrodynamics from the Boltzmann equation, Physics of Fluids, 11 (1999), No. 8, 2354–2366. (See Section V).

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