From Boltzmann to Euler: Hilbert's 6th problem revisited

DOI10.1016/j.camwa.2012.08.016zbMath1382.76215OpenAlexW2003747389WikidataQ56386649 ScholiaQ56386649MaRDI QIDQ2629457

Marshall Slemrod

Publication date: 6 July 2016

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.camwa.2012.08.016

zbMATH Keywords

Boltzmann equationChapman-Enskog expansion

Mathematics Subject Classification ID

Rarefied gas flows, Boltzmann equation in fluid mechanics (76P05) Gas dynamics (general theory) (76N15) Euler equations (35Q31) Boltzmann equations (35Q20)

Related Items (17)

Editorial: Grasping complexity ⋮ The Problem with Hilbert’s 6th Problem ⋮ Molecular extended thermodynamics of rarefied polyatomic gases and wave velocities for increasing number of moments ⋮ From Newton to Navier–Stokes, or how to connect fluid mechanics equations from microscopic to macroscopic scales ⋮ Chemotaxis and cross-diffusion models in complex environments: Models and analytic problems toward a multiscale vision ⋮ On a limit of perturbed conservation laws with saturating diffusion and non-positive dispersion ⋮ Virus models in complex frameworks: Towards modeling space patterns of SARS-CoV-2 epidemics ⋮ Cross-diffusion models in complex frameworks from microscopic to macroscopic ⋮ Spectral analysis and hydrodynamic manifolds for the linearized Shakhov model ⋮ Extended thermodynamics of rarefied polyatomic gases and characteristic velocities ⋮ Proof Verification Technology and Elementary Physics ⋮ Hilbert’s sixth problem and the failure of the Boltzmann to Euler limit ⋮ Hilbert’s sixth problem: the endless road to rigour ⋮ Convergence of a family of perturbed conservation laws with diffusion and non-positive dispersion ⋮ Hilbert’s 6th Problem: exact and approximate hydrodynamic manifolds for kinetic equations ⋮ Thermal creep of a rarefied gas on the basis of non-linear Korteweg-theory ⋮ A multiscale view of nonlinear diffusion in biology: From cells to tissues

Cites Work

• Unnamed Item
• Hydrodynamic limits of the Boltzmann equation
• On the thermomechanics of interstitial working
• Hyperbolic principal subsystems: Entropy convexity and subcharacteristic conditions
• Chapman-Enskog $⇒$ viscosity-capillarity
• The small dispersion limit of the Korteweg-de Vries equation. I
• Convergence of solution to nonlinear dispersive equations
• Hydrodynamics from Grad's equations: What can we learn from exact solutions?

This page was built for publication: From Boltzmann to Euler: Hilbert's 6th problem revisited