ENGLISH

From hyperbolic systems to kinetic theory: a personalized quest

By Luc Tartar

Book information

Publisher
Springer
Year
2008
ISBN
3540775617, 9783540775614
Open Library ID
OL18732214M
Language
english
Format
PDF
Filesize
2 MB (2228881 bytes)
Series
Lecture Notes of the Unione Matematica Italiana
Edition
1
Pages
294\294
Library
Kolxo3
Time added
2009-07-20 03:45:11

Description

Equations of state are not always effective in continuum mechanics. Maxwell and Boltzmann created a kinetic theory of gases, using classical mechanics. How could they derive the irreversible Boltzmann equation from a reversible Hamiltonian framework? By using probabilities, which destroy physical reality! Forces at distance are non-physical as we know from Poincar?'s theory of relativity. Yet Maxwell and Boltzmann only used trajectories like hyperbolas, reasonable for rarefied gases, but wrong without bound trajectories if the "mean free path between collisions" tends to 0. Tartar relies on his H-measures, a tool created for homogenization, to explain some of the weaknesses, e.g. from quantum mechanics: there are no "particles", so the Boltzmann equation and the second principle, can not apply. He examines modes used by energy, proves which equation governs each mode, and conjectures that the result will not look like the Boltzmann equation, and there will be more modes than those indexed by velocity!

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