Global solutions to the Cauchy problem for the relativistic Boltzmann equation with near-vacuum data

DOI10.1007/s00220-006-1522-yzbMath1107.82047OpenAlexW2027242339MaRDI QIDQ865063

Robert T. Glassey

Publication date: 13 February 2007

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00220-006-1522-y

zbMATH Keywords

relativistic Boltzmann equationcollision operatorscattering cross sectionnear-vacuum

Mathematics Subject Classification ID

Rarefied gas flows, Boltzmann equation in fluid mechanics (76P05) PDEs in connection with relativity and gravitational theory (35Q75) Kinetic theory of gases in time-dependent statistical mechanics (82C40) Quantum hydrodynamics and relativistic hydrodynamics (76Y05) Initial value problems for nonlinear first-order PDEs (35F25)

Related Items

Global existence of the classical solutions for the inhomogeneous relativistic Boltzmann equation near vacuum in the Robertson-Walker space-time, Global solution to the relativistic Enskog equation with near-vacuum data, Distributional and classical solutions to the Cauchy Boltzmann problem for soft potentials with Integrable angular cross section, Uniform stability of the solutions to the relativistic Enskog equation, Asymptotic behaviour of the relativistic Boltzmann equation in the Robertson-Walker spacetime, Global existence for the relativistic Enskog equations, Stability of the relativistic Vlasov-Maxwell-Boltzmann system for short range interaction, Asymptotic stability of the relativistic Boltzmann equation for the soft potentials, Inhomogeneous relativistic Boltzmann equation near vacuum in the Robertson-Walker space-time, The relativistic Boltzmann equation on a spherically symmetric gravitational field, Momentum regularity and stability of the relativistic Vlasov-Maxwell-Boltzmann system, Asymptotic-stability of the inhomogeneous Boltzmann equation in the Robertson–Walker space–time with Israel particles, Non-negativity of the solution of the Boltzmann equation in a curved space-time, Global well-posedness of a binary-ternary Boltzmann equation, On the emergence of quantum Boltzmann fluctuation dynamics near a Bose-Einstein condensate, The coupled Yang-Mills-Boltzmann system in Bianchi type I space-time, Propagation of \(L^p\) estimates for the spatially homogeneous relativistic Boltzmann equation, The relativistic Vlasov-Maxwell-Boltzmann system for short range interaction, Future global existence and asymptotic behaviour of solutions to the Einstein-Boltzmann system with Bianchi I symmetry, Global existence proof for relativistic Boltzmann equation with hard interactions, On the relativistic BGK-Boltzmann model: asymptotics and hydrodynamics, The Einstein-Vlasov system/kinetic theory, Global Well-Posedness of the Relativistic Boltzmann Equation, Propagation of uniform upper bounds for the spatially homogeneous relativistic Boltzmann equation, UNIFORM L²-STABILITY ESTIMATES FOR THE RELATIVISTIC BOLTZMANN EQUATION, The relativistic Enskog equation near the vacuum in the Robertson-Walker space-time, Stability of global solution for the relativistic Enskog equation near vacuum, Uniform stability of the Boltzmann equation with an external force near vacuum, The spatially homogeneous Boltzmann equation for massless particles in an FLRW background, An inverse problem for the relativistic Boltzmann equation, Global existence theorem of mild solutions of the Boltzmann equation for short range interactions

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The relativistic Boltzmann equation: Theory and applications
• On the Cauchy problem of the Boltzmann equation with a soft potential
• On the Cauchy problem for Boltzmann equations: Global existence and weak stability
• The Boltzmann equation: global existence for a rare gas in an infinite vacuum
• The Boltzmann equation with a soft potential. I: Linear, spatially- homogeneous
• Global classical solutions of the Vlasov-Poisson system in three dimensions for general initial data
• Initial-boundary value problems for the Boltzmann equation: Global existence of weak solutions
• Global existence proof for relativistic Boltzmann equation
• The Boltzmann equation and its applications
• Global solutions to the initial value problem for the nonlinear Boltzmann equation
• The Boltzmann equation. I. Uniqueness and local existence
• The mathematical theory of dilute gases
• Compactness in Boltzmann's equation via Fourier integral operators and applications. I, II
• The Vlasov-Maxwell-Boltzmann system near Maxwellians
• Classical solutions to the Boltzmann equation for molecules with an angular cutoff
• Classical solution of the nonlinear Boltzmann equation in all \({\mathbb{R}}^ 3\): asymptotic behavior of solutions.
• Asymptotic stability of the relativistic Maxwellian
• On blowup for gain-term-only classical and relativistic Boltzmann equations
• The Boltzmann equation and thirteen moments
• On the classical solutions of the boltzmann equation
• Global existence of smooth solutions to the vlasov poisson system in three dimensions
• On the existence of global solutions of mixed problem for non-linear Boltzmann equation
• On the derivatives of the collision map of relativistic particles
• Asymptotic stability of the relativistic Maxwellian via fourteen moments
• Regularity of the Gain Term and Strong $L^1 $ Convergence to Equilibrium for the Relativistic Boltzmann Equation
• On the Cauchy problem for the nonlinear Boltzmann equation global existence uniqueness and asymptotic stability
• The Einstein-Vlasov system/kinetic theory
• The Vlasov-Poisson-Boltzmann system near vacuum