Classical solution of the nonlinear Boltzmann equation in all \({\mathbb{R}}^ 3\): asymptotic behavior of solutions.

DOI10.1007/BF01026493zbMath1084.82545OpenAlexW2046498313MaRDI QIDQ1963557

Jacek Polewczak

Publication date: 2 February 2000

Published in: Journal of Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01026493

zbMATH Keywords

Boltzmann equationinitial value problemkinetic theoryasymptotic behavior of solutions

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Rarefied gas flows, Boltzmann equation in fluid mechanics (76P05) Kinetic theory of gases in time-dependent statistical mechanics (82C40) Kinetic theory of gases in equilibrium statistical mechanics (82B40)

Related Items (31)

Stability of vacuum for the Boltzmann equation with moderately soft potentials ⋮ On a time and space discretized approximation of the Boltzmann equation in the whole space ⋮ Stability estimates of the Boltzmann equation in a half space ⋮ Global existence and stability of mild solutions to the Boltzmann system for gas mixtures ⋮ Global solutions to the Cauchy problem for the relativistic Boltzmann equation with near-vacuum data ⋮ On the initial value problem for the Boltzmann equation with a force term ⋮ New estimations of the nonlinear Boltzmann operator and their application to existence theorems ⋮ Well-posedness and scattering for the Boltzmann equations: soft potential with cut-off ⋮ Global classical solution to the inelastic Boltzmann equation with potential force ⋮ Global well-posedness of a binary-ternary Boltzmann equation ⋮ Microscopic solutions of kinetic equations and the irreversibility problem ⋮ On the Cauchy problem for the inelastic Boltzmann equation with external force ⋮ Uniform stability estimates for solutions and their gradients to the Boltzmann equation: a unified approach ⋮ Nonlinear functionals of the Boltzmann equation and uniform stability estimates ⋮ \(L^1\) stability of the Boltzmann equation for the hard-sphere model ⋮ \(L^{1}\) and BV-type stability of the Boltzmann equation with external forces ⋮ Stability of vacuum for the Landau equation with moderately soft potentials ⋮ \(L ^{1}\) and BV-type stability of the inelastic Boltzmann equation near vacuum ⋮ UNIFORM L^p-STABILITY ESTIMATE FOR THE SPATIALLY INHOMOGENEOUS BOLTZMANN EQUATION NEAR VACUUM ⋮ Uniform \(L^{1}\)-stability estimate of the Boltzmann equation near a local Maxwellian ⋮ Stability and modeling error for the Boltzmann equation ⋮ Global existence and stability of mild solutions to the inelastic Boltzmann system for gas mixtures ⋮ Global existence of classical solutions to the inelastic Vlasov-Poisson-Boltzmann system ⋮ Macroscopic regularity for the Boltzmann equation ⋮ UNIFORM L²-STABILITY ESTIMATES FOR THE RELATIVISTIC BOLTZMANN EQUATION ⋮ New properties of a class of generalized kinetic equations ⋮ L¹STABILITY FOR THE VLASOV–POISSON–BOLTZMANN SYSTEM AROUND VACUUM ⋮ Stability of global solution for the relativistic Enskog equation near vacuum ⋮ On the inelastic Enskog equation near vacuum ⋮ Uniform stability of the Boltzmann equation with an external force near vacuum ⋮ Global existence to Boltzmann equation with external force in infinite vacuum

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The Boltzmann equation: global existence for a rare gas in an infinite vacuum
• On the nonlinear Boltzmann equation in unbounded domains
• The Boltzmann equation. I. Uniqueness and local existence
• Existence in the large and asymptotic behaviour for the Boltzmann equation
• On the Cauchy problem for the nonlinear Boltzmann equation global existence uniqueness and asymptotic stability

This page was built for publication: Classical solution of the nonlinear Boltzmann equation in all \({\mathbb{R}}^ 3\): asymptotic behavior of solutions.