On the convergence of solutions of the enskog equation to solutions of the boltzmann equation

DOI10.1080/03605308908820644zbMath0688.76053OpenAlexW1985269837MaRDI QIDQ4207736

Leif Arkeryd, Carlo Cercignani

Publication date: 1989

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03605308908820644

zbMATH Keywords

Boltzmann equationexistence theoremweak convergence of solutionsEnskog equation with a symmetrized kernelinitial data with finite mass, energy and entropy

Mathematics Subject Classification ID

Rarefied gas flows, Boltzmann equation in fluid mechanics (76P05) Kinetic theory of gases in equilibrium statistical mechanics (82B40)

Related Items (19)

A large data existence result for the stationary Boltzmann equation in a cylindrical geometry ⋮ Uniform stability of the solutions to the relativistic Enskog equation ⋮ Global existence for the relativistic Enskog equations ⋮ From kinetic to Navier-Stokes-type equations ⋮ The Enskog process ⋮ On the StrongL¹Trend to Equilibrium for the Boltzmann Equation ⋮ Microscopic solutions of the Boltzmann-Enskog equation in the series representation ⋮ Global existence in \(L^ 1\) for the Enskog equation and convergence of the solutions to solutions of the Boltzmann equation ⋮ On the modified Enskog equation for elastic and inelastic collisions. Models with spin ⋮ Microscopic solutions of kinetic equations and the irreversibility problem ⋮ Unnamed Item ⋮ Derivation of the particle dynamics from kinetic equations ⋮ Global weak solutions and uniform \(L^p\)-stability of the Boltzmann-Enskog equation ⋮ THE BOLTZMANN–ENSKOG EQUATION NEAR MAXWELLIANS ⋮ Unnamed Item ⋮ The relativistic Enskog equation near the vacuum in the Robertson-Walker space-time ⋮ Ionization and recombination in plasmas ⋮ A global existence theorem for the initial-boundary-value problem for the Boltzmann equation when the boundaries are not isothermal ⋮ Microscopic and soliton-like solutions of the Boltzmann-Enskog and generalized Enskog equations for elastic and inelastic hard spheres

Cites Work

• On the Cauchy problem for Boltzmann equations: Global existence and weak stability
• Loeb solutions of the Boltzmann equation
• Regularity of the moments of the solution of a transport equation
• The Boltzmann equation and its applications
• Small data existence for the Enskog equation in \(L^ 1\).
• On the asymptotic equivalence between the Enskog and the Boltzmann equations.
• On the Enskog Equation with Large Initial Data
• Existence of global solutions for the space inhomogeneous Enskog equation
• On the Enskog equation in two space variables

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