Steady solutions of the Boltzmann equation for a gas flow past an obstacle. I: Existence

DOI10.1007/BF00281521zbMath0538.76070OpenAlexW2011136135MaRDI QIDQ793608

Kiyoshi Asano, Seiji Ukai

Publication date: 1983

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00281521

zbMATH Keywords

boundary conditionsstationary flowspecular reflectionconvex obstacleperturbed problemdiffusion reflectionMaxwellian distribution at infinitynonlinar

Mathematics Subject Classification ID

Rarefied gas flows, Boltzmann equation in fluid mechanics (76P05) Kinetic theory of gases in equilibrium statistical mechanics (82B40)

Related Items (25)

The Boltzmann equation with frictional force ⋮ A large data existence result for the stationary Boltzmann equation in a cylindrical geometry ⋮ Existence of Solutions to the Stationary Linear Boltzmann Equation ⋮ Steady solutions of the Boltzmann equation for a gas flow past an obstacle. II. Stability ⋮ Stability estimates of the Boltzmann equation in a half space ⋮ Asymptotic theory of a uniform flow of a rarefied gas past a sphere at low Mach numbers ⋮ A boundary value problem for discrete-velocity models ⋮ Local solutions in gevrey classes to the nonlinear Boltzmann equation without cutoff ⋮ The global existence and large time behavior of smooth compressible fluid in an infinitely expanding ball. III: The 3-D Boltzmann equation ⋮ Stationary non equilibrium states in kinetic theory ⋮ Hypocoercivity for perturbation theory and perturbation of hypocoercivity for confined Boltzmann-type collisional equations ⋮ Exterior problem for the Boltzmann equation with temperature difference: asymptotic stability of steady solutions ⋮ Unnamed Item ⋮ Hydrodynamic limit of a kinetic gas flow past an obstacle ⋮ Initial-boundary value problems for the Boltzmann equation: Global existence of weak solutions ⋮ GLOBAL SOLUTIONS TO THE BOLTZMANN EQUATION WITH EXTERNAL FORCES ⋮ The stationary nonlinear Boltzmann equation in a Couette setting with multiple, isolated \(L^q\)-solutions and hydrodynamic limits ⋮ \(L^1\) solutions to the stationary Boltzmann equation in a slab ⋮ Stationary Boltzmann's Equation With a Source Term ⋮ Applications of the Boltzmann equation within the context of upper atmosphere vehicle aerodynamics ⋮ Unnamed Item ⋮ Mathematical tools for kinetic equations ⋮ The Boltzmann equation: Flow of cloud of gas past a body ⋮ Exterior Problem of the Linear Vlasov--Poisson--Boltzmann System ⋮ Existence and uniqueness for nonlinear boundary value problems in kinetic theory

Cites Work

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• Initial boundary value problems for the equations of motion of compressible viscous and heat-conductive fluids
• On the initial boundary value problem of the linearized Boltzmann equation in an exterior domain
• The hodograph method in fluid-dynamics in the light of variational inequalities
• The Boltzmann equation. I. Uniqueness and local existence
• The first and second fluid approximation to the linearized Boltzmann equation
• Asymptotic Theory of the Boltzmann Equation

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