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gallagher i from newton boltzmann hard spheres short range potentials 2013

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Textbook in PDF format The subject of this monograph is the appearance of irreversibility in gas dynamics. At a molecular level, the dynamics is Newtonian. In particular, it is reversible, in contrast with observations at a macroscopic level. We provide a rigorous derivation of the Boltzmann equation as the mesoscopic limit of systems of hard spheres, or Newtonian particles interacting via a short-range potential, as the number of particles N goes to infinity and the characteristic length of interaction ε simultaneously goes to 0, in the Boltzmann-Grad scaling Nεd−1 ≡ 1. The time of validity of the convergence is a fraction of the average time of first collision, due to a limitation of the time on which one can prove uniform estimates for the BBGKY and Boltzmann hierarchies. Our proof relies on the fundamental ideas of Lanford, and the important contributions of King, Cercignani, Illner and Pulvirenti, and Cercignani, Gerasimenko and Petrina. The main novelty here is the detailed study of pathological trajectories involving recollisions, which proves the term-by-term convergence for the correlation series expansion. Preface I Introduction The low density limit The Boltzmann equation Main results II The case of hard spheres Microscopic dynamics and BBGKY hierarchy Uniform a priori estimates for the BBGKY and Boltzmann hierarchies Statement of the convergence result Strategy of the proof of convergence III The case of short-range potentials Two-particle interactions Truncated marginals and the BBGKY hierarchy Cluster estimates and uniform a priori estimates Convergence result and strategy of proof IV Termwise convergence Elimination of recollisions Truncated collision integrals Proof of convergence Concluding remarks

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Gallagher I. From Newton to Boltzmann. Hard Spheres..Short-range Potentials 2013.pdf 1.2 MB

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gallagher i from newton boltzmann hard spheres short range potentials 2013

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