Title page for ETD etd-10242005-124058


Type of Document Dissertation
Author Liu, Rongsheng
URN etd-10242005-124058
Title Global existence in L1 for the square-well kinetic equation
Degree PhD
Department Mathematics
Advisory Committee
Advisor Name Title
Greenberg, William Committee Chair
Beattie, Christopher A. Committee Member
Hagedorn, George A. Committee Member
Klaus, Martin Committee Member
Zweifel, Paul F. Committee Member
Keywords
  • Kinetic theory of gases Mathematical models
Date of Defense 1993-04-04
Availability restricted
Abstract

An attractive square-well is incorporated into the Enskog equation, in order to model the' kinetic theory of a moderately dense gas with intermolecular potential. The existence of solutions to the Cauchy problem in L 1. global in time and for arbitrary initial data. is proved.

A simple derivation of the square-well kinetic equation is given. Lewis's method is used~ which starts from the Liouville equation of statistical mechanics. Then various symmetries of the collisional integrals are established. An H-theorem for entropy, mass, and momentum conservation is obtained, as well as an energy estimate, and key gain-loss estimates.

Approximate equations for the square-well kinetic equatioll are constructed that preserve symmetries of the collisional integral. Existence of nonnegative solutions of the approximate equations and weak compactness are obtained. The velocity averaging lemma of Golse is then a principal tool in demonstrating the convergence of the approximate solutions to a solution of the renormalized square well kinetic equation. The existence of weak solution of the irutial value problem for the squarewell kinetic equation is thus proved.

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