The Cauchy problem for the BGK equation with an external force

DOI10.1016/J.JMAA.2012.02.039zbMath1236.35100OpenAlexW1965192503MaRDI QIDQ413214

Jinbo Wei, Xian-Wen Zhang

Publication date: 4 May 2012

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2012.02.039

zbMATH Keywords

BGK equationexternal force\(L^{1}\) solution\(L^{p}\) solution

Mathematics Subject Classification ID

A priori estimates in context of PDEs (35B45) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Boltzmann equations (35Q20)

Related Items (8)

On quantitative hypocoercivity estimates based on Harris-type theorems ⋮ On the BGK equation with some force fields in \(L^p\) space ⋮ Quantum BGK Model near a Global Fermi--Dirac Distribution ⋮ Cauchy problem for the ellipsoidal BGK model for polyatomic particles ⋮ Ellipsoidal BGK model for polyatomic molecules near Maxwellians: a dichotomy in the dissipation estimate ⋮ Entropy production for ellipsoidal BGK model of the Boltzmann equation ⋮ Existence theorems for the initial value problem of the cometary flow equation with an external force ⋮ On the Cauchy problem for Wigner-Poisson-BGK equation in the Wiener algebra

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the Cauchy problem of the Vlasov-Poisson-BGK system: global existence of weak solutions
• A global existence theorem for the nonlinear BGK equation
• The BGK model with external confining potential: existence, long-time behaviour and time-periodic Maxwellian equilibria
• Boltzmann equation with external force and Vlasov-Poisson-Boltzmann system in infinite vacuum
• Global existence to the BGK model of Boltzmann equation
• On the Cauchy problem for Boltzmann equations: Global existence and weak stability
• Local solutions to the initial and initial boundary value problem for the Boltzmann equation with an external force. I
• Some remarks about continuity properties of local Maxwellians and an existence theorem for the BGK model of the Boltzmann equation
• Regularity of the moments of the solution of a transport equation
• The Boltzmann equation and its applications
• Weighted \(L^ \infty\) bounds and uniqueness for the Boltzmann BGK model
• The Vlasov-Maxwell-Boltzmann system near Maxwellians
• Uniqueness for the BGK-equation in \(\mathbb{R}^ N\) and rate of convergence for a semi-discrete scheme
• \(L^{1}\) and BV-type stability of the Boltzmann equation with external forces
• On solution of the nonlinear Boltzmann equation with a cut-off in an unbounded domain
• GLOBAL SOLUTIONS TO THE BOLTZMANN EQUATION WITH EXTERNAL FORCES
• Global existence to Boltzmann equation with external force in infinite vacuum
• On the initial value problem for the Boltzmann equation with a force term
• L p solutions to the Cauchy problem of the BGK equation
• The Vlasov‐Poisson‐Boltzmann system near Maxwellians
• Cauchy problem for the Boltzmann-BGK model near a global Maxwellian
• A Model for Collision Processes in Gases. I. Small Amplitude Processes in Charged and Neutral One-Component Systems
• The Vlasov-Poisson-Boltzmann system near vacuum

This page was built for publication: The Cauchy problem for the BGK equation with an external force