Global existence in L sup 1 for the modified nonlinear Enskog equation in R sup 3

Journal Article · Sat Jul 01 00:00:00 EDT 1989 · Journal of Statistical Physics; (USA)

DOI:https://doi.org/10.1007/BF01044239· OSTI ID:7165838

Polewczak, J ^[1]

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1. Virginia Polytechnic Institute and State Univ., Blacksburg (USA)

A global existence theorem with large initial data in L{sup 1} is given for the modified Enskog equation in R{sup 3}. The method, which is based on the existence of a Liapunov functional (analog of the H-Boltzmann theorem), utilizes a weak compactness argument in L{sup 1} in a similar way to the DiPerna-Lions proof for the Boltzmann equation. The existence theorem is obtained under certain condition on the behavior of the geometric factor Y. The condition on Y amounts to the fact that the L{sup 1} norm of the collision term grows linearly when the local density tends to infinity.

• OSTI ID: 7165838
• Journal Information: Journal of Statistical Physics; (USA), Vol. 56:1-2; ISSN 0022-4715
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
TRANSPORT THEORY
STATISTICAL MECHANICS
BOLTZMANN EQUATION
BOUNDARY CONDITIONS
CAUCHY PROBLEM
DISTRIBUTION FUNCTIONS
GASES
GEOMETRY
HARD-SPHERE MODEL
KINETICS
LYAPUNOV METHOD
MATHEMATICAL MANIFOLDS
MATHEMATICAL SPACE
MOLECULE COLLISIONS
MOLECULES
NONLINEAR PROBLEMS
RENORMALIZATION
COLLISIONS
DIFFERENTIAL EQUATIONS
EQUATIONS
FLUIDS
FUNCTIONS
MATHEMATICS
MECHANICS
PARTIAL DIFFERENTIAL EQUATIONS
SPACE
645201* - High Energy Physics- Particle Interactions & Properties-Theoretical- General & Scattering Theory
657002 - Theoretical & Mathematical Physics- Classical & Quantum Mechanics