The Boltzmann Equation with Incoming Boundary Condition: Global Solutions and Navier--Stokes Limit

DOI10.1137/17M114697XzbMath1419.76566arXiv1701.04144MaRDI QIDQ5231317

Ning Jiang, Xu Zhang

Publication date: 26 August 2019

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1701.04144

zbMATH Keywords

Boltzmann equationNavier-Stokes limitincoming data

Mathematics Subject Classification ID

Rarefied gas flows, Boltzmann equation in fluid mechanics (76P05) Boundary value problems for nonlinear first-order PDEs (35F30) Boltzmann equations (35Q20)

Related Items (3)

Positive solutions and hydrodynamic limit of the steady Boltzmann equation with in-flow boundary ⋮ Global renormalized solutions and Navier-Stokes limit of the Boltzmann equation with incoming boundary condition for long range interaction ⋮ Collisional sheath solutions of a bi-species Vlasov-Poisson-Boltzmann boundary value problem

Cites Work

• Unnamed Item
• Unnamed Item
• Molecular gas dynamics. Theory, techniques, and applications.
• On the Cauchy problem for Boltzmann equations: Global existence and weak stability
• From the Boltzmann equation to an incompressible Navier-Stokes-Fourier system
• The incompressible Navier-Stokes limit of the Boltzmann equation for hard cutoff potentials
• On the initial-boundary value problem for the Boltzmann equation
• Initial-boundary value problems for the Boltzmann equation: Global existence of weak solutions
• The Boltzmann equation and its applications
• The mathematical theory of dilute gases
• The Navier-Stokes limit of the Boltzmann equation for bounded collision kernels
• Convergence of solutions to the Boltzmann equation in the incompressible Euler limit
• The acoustic limit for the Boltzmann equation
• Velocity averaging in \(L^1\) for the transport equation
• Compactness in Boltzmann's equation via Fourier integral operators and applications. III
• Kinetic theory and fluid dynamics
• From Boltzmann's equation to the incompressible Navier-Stokes-Fourier system with long-range interactions
• Global renormalized solutions and Navier-Stokes limit of the Boltzmann equation with incoming boundary condition for long range interaction
• Boundary Layers and Incompressible Navier-Stokes-Fourier Limit of the Boltzmann Equation in Bounded Domain I
• Kinetic equations with Maxwell boundary conditions
• The milne and kramers problems for the boltzmann equation of a hard sphere gas
• Fluid dynamic limits of kinetic equations II convergence proofs for the boltzmann equation
• From the Boltzmann equation to the Stokes-Fourier system in a bounded domain
• On The Trace Problem For Solutions Of The Vlasov Equation
• On the Boltzmann equation for long-range interactions
• Stokes-Fourier and acoustic limits for the Boltzmann equation: Convergence proofs
• Remarks on the Acoustic Limit for the Boltzmann Equation
• On the initial boundary value problem for the Vlasov-Poisson-Boltzmann system
• From the Boltzmann equations to the equations of incompressible fluid mechanics. I, II

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