On the modified Enskog equation for elastic and inelastic collisions. Models with spin

DOI10.1016/S0294-1449(16)30265-7zbMath0850.70141OpenAlexW2275575902MaRDI QIDQ1177838

Maria J. Esteban, Perthame, Benoît

Publication date: 26 June 1992

Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)

Full work available at URL: http://www.numdam.org/item?id=AIHPC_1991__8_3-4_289_0

zbMATH Keywords

spinrenormalized solutionselastic collisionsinelastic collisionsmodified Enskog equation

Mathematics Subject Classification ID

Rarefied gas flows, Boltzmann equation in fluid mechanics (76P05) Kinetic theory of gases in time-dependent statistical mechanics (82C40) PDEs in connection with statistical mechanics (35Q82)

Related Items (21)

GENERALIZED KINETIC (BOLTZMANN) MODELS: MATHEMATICAL STRUCTURES AND APPLICATIONS ⋮ Fast spectral solution of the generalized Enskog equation for dense gases ⋮ Uniform stability of the solutions to the relativistic Enskog equation ⋮ Global existence for the relativistic Enskog equations ⋮ Nonlinear kinetic equations with dissipative collisions ⋮ FROM THE MATHEMATICAL KINETIC THEORY TO MODELLING COMPLEX SYSTEMS IN APPLIED SCIENCES ⋮ From the Boltzmann equation to generalized kinetic models in applied sciences ⋮ Viscosity analysis on the Boltzmann equation ⋮ Unnamed Item ⋮ On the hydrodynamic limit of the Enskog equation ⋮ Global weak solutions and uniform \(L^p\)-stability of the Boltzmann-Enskog equation ⋮ Is the linearized Boltzmann-Enskog operator dissipative? ⋮ The Cauchy problem for the generalized Boltzmann equation with dissipative collisions. ⋮ \(L ^{1}\) and BV-type stability of the inelastic Boltzmann equation near vacuum ⋮ The Boltzmann equation for dissipative disparate mixtures ⋮ Non-equilibrium dynamics of dense gas under tight confinement ⋮ New properties of a class of generalized kinetic equations ⋮ Stability of global solution for the relativistic Enskog equation near vacuum ⋮ On the inelastic Enskog equation near vacuum ⋮ Incompressible Navier-Stokes limit for the Enskog equation ⋮ A BGK model for a suspension of inelastic spheres

Cites Work

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• Loeb solutions of the Boltzmann equation
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• Regularity of the moments of the solution of a transport equation
• Global existence in \(L^ 1\) for the Enskog equation and convergence of the solutions to solutions of the Boltzmann 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.
• Global existence in \(L^ 1\) for the generalized Enskog equation.
• Global existence in \(L^ 1\) for the modified nonlinear Enskog equation in \({\mathbb{R}}^ 3\)
• Global weak solutions of Vlasov‐Maxwell systems
• On the Enskog Equation with Large Initial Data
• SOME MATHEMATICAL RESULTS ON THE ASYMPTOTIC BEHAVIOUR OF THE SOLUTIONS TO THE INITIAL VALUE PROBLEM FOR THE ENSKOG EQUATION
• Existence of global solutions for the space inhomogeneous Enskog equation
• On the convergence of solutions of the enskog equation to solutions of the boltzmann equation

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