On the convergence of smooth solutions from Boltzmann to Navier-Stokes

DOI10.5802/ahl.40zbMath1448.35393arXiv1903.02214OpenAlexW2998283448MaRDI QIDQ2202468

Isabelle Gallagher, Isabelle Tristani

Publication date: 18 September 2020

Published in: Annales Henri Lebesgue (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1903.02214

zbMATH Keywords

Boltzmann equationNavier-Stokes equation

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Navier-Stokes equations for incompressible viscous fluids (76D05) Navier-Stokes equations (35Q30) Kinetic theory of gases in time-dependent statistical mechanics (82C40) Statistical mechanics of gases (82D05) Kinetic theory of gases in equilibrium statistical mechanics (82B40) Strong solutions to PDEs (35D35) Boltzmann equations (35Q20)

Related Items (9)

Regularization estimates and hydrodynamical limit for the Landau equation ⋮ Hydrodynamic Limit of 3dimensional Evolutionary Boltzmann Equation in Convex Domains ⋮ Hydrodynamic limit of Boltzmann equations for gas mixture ⋮ Convergence from the two-species Vlasov-Poisson-Boltzmann system to the two-fluid incompressible Navier-Stokes-Fourier-Poisson system with Ohm's law ⋮ On the Convergence from Boltzmann to Navier–Stokes–Fourier for General Initial Data ⋮ Hypocoercivity for perturbation theory and perturbation of hypocoercivity for confined Boltzmann-type collisional equations ⋮ Hypocoercivity for kinetic linear equations in bounded domains with general Maxwell boundary condition ⋮ The compressible Euler and acoustic limits from quantum Boltzmann equation with Fermi-Dirac statistics ⋮ A spectral study of the linearized Boltzmann operator in \(L^2\)-spaces with polynomial and Gaussian weights

Cites Work

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• From the Boltzmann equation to the incompressible Navier-Stokes equations on the torus: a quantitative error estimate
• On the Cauchy problem for Boltzmann equations: Global existence and weak stability
• From the Boltzmann equation to an incompressible Navier-Stokes-Fourier system
• Hydrodynamic limits of the Boltzmann equation
• The incompressible Navier-Stokes limit of the Boltzmann equation for hard cutoff potentials
• \(L^ 2\) decay for weak solutions of the Navier-Stokes equations
• Fluid dynamical limit of the nonlinear Boltzmann equation to the level of the compressible Euler equation
• Fast singular limits of hyperbolic PDEs
• Oscillatory perturbations of the Navier-Stokes equations
• Asymptotics and stability for global solutions to the Navier-Stokes equations.
• The Navier-Stokes limit of the Boltzmann equation for bounded collision kernels
• Étude de diverses équations intégrales non linéaires et de quelques problèmes que pose l'hydrodynamique
• The first and second fluid approximation to the linearized Boltzmann equation
• Flows of non-Lipschitzian vector fields and Navier-Stokes equations
• On the Navier-Stokes initial value problem. I
• ON NONNEGATIVITY OF SOLUTIONS OF THE BOLTZMANN EQUATION
• Incompressible navier-stokes and euler limits of the boltzmann equation
• Fourier Analysis and Nonlinear Partial Differential Equations
• On the global wellposedness of the 3-D Navier–Stokes equations with large initial data
• The Navier-Stokes Problem in the 21st Century
• Large, global solutions to the Navier-Stokes equations, slowly varying in one direction
• On the initial layer and the existence theorem for the nonlinear Boltzmann equation
• Decay Results for Weak Solutions of the Navier-Stokes Equations on Rⁿ
• The fluid dynamic limit of the nonlinear boltzmann equation
• THE CLASSICAL INCOMPRESSIBLE NAVIER-STOKES LIMIT OF THE BOLTZMANN EQUATION
• Remarques sur l’Existence Globale Pour le Système de Navier–Stokes Incompressible
• Acoustic and Stokes limits for the Boltzmann equation
• Fluid dynamic limits of kinetic equations II convergence proofs for the boltzmann equation
• Large Time Behaviour of Solutions to the Navier-Stokes Equations in H Spaces
• From Boltzmann to incompressible Navier–Stokes in Sobolev spaces with polynomial weight
• Fluids with anisotropic viscosity
• Boltzmann diffusive limit beyond the Navier‐Stokes approximation
• THE BOLTZMANN EQUATION IN THE SPACE $L^2\cap L^\infty_\beta$: GLOBAL AND TIME-PERIODIC SOLUTIONS
• Quantitative perturbative study of convergence to equilibrium for collisional kinetic models in the torus
• From the Boltzmann equations to the equations of incompressible fluid mechanics. I, II

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