On the relativistic BGK-Boltzmann model: asymptotics and hydrodynamics

DOI10.1007/s10955-012-0600-0zbMath1264.82111arXiv1205.6603OpenAlexW3098955012MaRDI QIDQ691015

Juan Soler, Juanjo Nieto, Abdelghani Bellouquid, Juan G. Calvo

Publication date: 29 November 2012

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

Full work available at URL: https://arxiv.org/abs/1205.6603

zbMATH Keywords

dynamicsBoltzmann equationBBGKY hierarchymaximum entropykinetic theorylinearized operatorgasBGKhydrodynamical limitsthermodynamical limitnonlinear solutionrelativistic evolution equation

Mathematics Subject Classification ID

Applications of functional analysis in biology and other sciences (46N60) Rarefied gas flows, Boltzmann equation in fluid mechanics (76P05) Transport processes in time-dependent statistical mechanics (82C70) Kinetic theory of gases in time-dependent statistical mechanics (82C40) Kinetic theory of gases in equilibrium statistical mechanics (82B40)

Related Items

Global existence and time decay of the relativistic BGK equation in the whole space ⋮ Propagation phenomena of the solution for the relativistic BGK model ⋮ On a Relativistic BGK Model for Polyatomic Gases Near Equilibrium ⋮ Relativistic BGK model for massless particles in the FLRW spacetime ⋮ The Euler Limit of the Relativistic Boltzmann Equation ⋮ Propagation of \(L^p\) estimates for the spatially homogeneous relativistic Boltzmann equation ⋮ Stationary Solutions to the Anderson--Witting Model of the Relativistic Boltzmann Equation in a Bounded Interval ⋮ Smooth solutions to the BGK equation and the ES-BGK equation with infinite energy ⋮ Hydrodynamic limits of kinetic equations for polyatomic and reactive gases ⋮ Global existence and asymptotic stability near equilibrium for the relativistic BGK model ⋮ Global existence and uniqueness to the Cauchy problem of the BGK equation with infinite energy ⋮ Propagation of uniform upper bounds for the spatially homogeneous relativistic Boltzmann equation ⋮ Global weak solutions to the relativistic BGK equation ⋮ Global existence of bounded solutions to the relativistic BGK model ⋮ Anderson-Witting model of the relativistic Boltzmann equation near equilibrium

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Hilbert expansion from the Boltzmann equation to relativistic fluids
• Asymptotic stability of the relativistic Boltzmann equation for the soft potentials
• The relativistic Boltzmann equation: Theory and applications
• Stability of the relativistic Maxwellian in a collisional plasma
• The formation of shocks in 3-dimensional fluids.
• Global solutions to the Cauchy problem for the relativistic Boltzmann equation with near-vacuum data
• Moment systems derived from relativistic kinetic equations
• Global existence to the BGK model of Boltzmann equation
• From Boltzmann's kinetic theory to Euler's equations
• Asymptotic behavior and orbital stability of galactic dynamics in relativistic scalar gravity
• Solution of the BGK model kinetic equation for very hard particle interaction
• On the linearized relativistic Boltzmann equation. I: Existence of solutions
• Global solutions to the initial value problem for the nonlinear Boltzmann equation
• Solution of the local mass problem in general relativity
• Fluid dynamical limit of the nonlinear Boltzmann equation to the level of the compressible Euler equation
• Second-order accurate kinetic schemes for the ultra-relativistic Euler equations.
• Kinetic schemes for the relativistic gas dynamics
• On the hyperbolicity and causality of the relativistic Euler system under the kinetic equation of state
• Problème de Cauchy pour le système intégro-différentiel d'Einstein-Liouville. (Cauchy problem for the Einstein-Liouville integro-differential system)
• Global Newtonian Limit for the Relativistic Boltzmann Equation near Vacuum
• The Newtonian limit of the relativistic Boltzmann equation
• Relativistic relaxation models for a simple gas
• Virial inequalities for steady states in relativistic galactic dynamics
• The fluid-dynamical limit of a nonlinear model boltzmann equation
• On the existence of global solutions of mixed problem for non-linear Boltzmann equation
• The Linearized Boltzmann Collision Operator for Cut-Off Potentials
• Fluid dynamic limits of kinetic equations II convergence proofs for the boltzmann equation
• Asymptotic stability of the relativistic Maxwellian via fourteen moments
• Unified first law of black-hole dynamics and relativistic thermodynamics
• The principle of least action in Milne's kinematical relativty
• Global Existence and Large-Time Behavior for BGK Model for a Gas with Non-constant Cross Section
• Almost Exponential Decay Near Maxwellian
• ON THE ASYMPTOTIC ANALYSIS OF KINETIC MODELS TOWARDS THE COMPRESSIBLE EULER AND ACOUSTIC EQUATIONS
• Theorem of Uniqueness and Local Stability for Liouville-Einstein Equations
• A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems
• Classical and quantum-wedge billiards