Hypocoercivity for kinetic linear equations in bounded domains with general Maxwell boundary condition

DOI10.4171/aihpc/44zbMath1521.35132arXiv2102.07709OpenAlexW3133451059MaRDI QIDQ6172265

Armand Bernou, Stéphane Mischler, Isabelle Tristani, Kleber Carrapatoso

Publication date: 19 July 2023

Published in: Annales de l'Institut Henri Poincaré. Analyse Non Linéaire (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2102.07709

zbMATH Keywords

Boltzmann equationPoincaré inequalityspectral gapconvergence to equilibriumkinetic equationsLandau equationhypocoercivityKorn inequality

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Rarefied gas flows, Boltzmann equation in fluid mechanics (76P05) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Kinetic theory of gases in time-dependent statistical mechanics (82C40) Boltzmann equations (35Q20)

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Cites Work

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• Fine scales of decay of operator semigroups
• Asymptotic stability of the Boltzmann equation with Maxwell boundary conditions
• Hypocoercivity for the linear Boltzmann equation with confining forces
• From the Boltzmann equation to the incompressible Navier-Stokes equations on the torus: a quantitative error estimate
• On the speed of approach to equilibrium for a collisionless gas
• Stabilization of the wave equation by the boundary
• Decay and continuity of the Boltzmann equation in bounded domains
• Perturbative theory for the Boltzmann equation in bounded domains with different boundary conditions
• Spectral gap and coercivity estimates for linearized Boltzmann collision operators without angular cutoff
• On the Cauchy problem for Boltzmann equations: Global existence and weak stability
• Trace theorems and spatial continuity properties for the solutions of the transport equation.
• Hypocoercivity for kinetic equations with linear relaxation terms
• Non-uniform stability for bounded semi-groups on Banach spaces
• Asymptotic behavior of degenerate linear transport equations
• The Boltzmann equation with a soft potential. I: Linear, spatially- homogeneous
• The Boltzmann equation with a soft potential. II: Nonlinear, spatially- periodic
• Initial-boundary value problems for the Boltzmann equation: Global existence of weak solutions
• Local energy decay of the wave equation in an exterior problem and without resonance in the neighborhood of the real line
• Spectral properties of hypoelliptic operators
• The Navier-Stokes limit of the Boltzmann equation for bounded collision kernels
• Geometric analysis of the linear Boltzmann equation. I: Trend to equilibrium
• Landau equation for very soft and Coulomb potentials near maxwellians
• On the trend to global equilibrium for spatially inhomogeneous kinetic systems: the Boltzmann equation
• Decay of the Boltzmann equation with the specular boundary condition in non-convex cylindrical domains
• Compactness in Boltzmann's equation via Fourier integral operators and applications. III
• Isotropic hypoelliptic and trend to equilibrium for the Fokker-Planck equation with a high-degree potential
• On diffuse reflection at the boundary for the Boltzmann equation and related equations
• The Landau equation with the specular reflection boundary condition
• Equilibrating effects of boundary and collision in rarefied gases
• The Fokker-Planck equation with subcritical confinement force
• Incompressible Navier-Stokes-Fourier limit from the Landau equation
• Hypocoercivity of linear kinetic equations via Harris's theorem
• On the convergence of smooth solutions from Boltzmann to Navier-Stokes
• A semigroup approach to the convergence rate of a collisionless gas
• The kinetic Fokker-Planck equation with weak confinement force
• Energy decay for a locally undamped wave equation
• On the convergence to equilibrium for degenerate transport problems
• Exponential decay for soft potentials near Maxwellian
• Explicit spectral gap estimates for the linearized Boltzmann and Landau operators with hard potentials
• Sharp polynomial decay rates for the damped wave equation on the torus
• Global solutions of Boltzmann's equation and the entropy inequality
• On the boundary-value problems of the theory of elasticity and Korn's inequality
• Correction to: ``The Landau equation with the specular reflection boundary condition
• Boundary Layers and Incompressible Navier-Stokes-Fourier Limit of the Boltzmann Equation in Bounded Domain I
• Incompressible navier-stokes and euler limits of the boltzmann equation
• Kinetic equations with Maxwell boundary conditions
• Hypocoercivity of linear degenerately dissipative kinetic equations
• Polynomial stability of operator semigroups
• Hypocoercivity
• THE CLASSICAL INCOMPRESSIBLE NAVIER-STOKES LIMIT OF THE BOLTZMANN EQUATION
• Fluid dynamic limits of kinetic equations II convergence proofs for the boltzmann equation
• Regularity and perturbation results for mixed second order elliptic problems
• On a variant of Korn's inequality arising in statistical mechanics
• From the Boltzmann equation to the Stokes-Fourier system in a bounded domain
• On The Trace Problem For Solutions Of The Vlasov Equation
• The Boltzmann Equation with Specular Boundary Condition in Convex Domains
• From Boltzmann to incompressible Navier–Stokes in Sobolev spaces with polynomial weight
• Incompressible Navier-Stokes-Fourier Limit from The Boltzmann Equation: Classical Solutions
• ANOTHER APPROACH TO LINEARIZED ELASTICITY AND A NEW PROOF OF KORN'S INEQUALITY
• The Vlasov‐Poisson‐Boltzmann system near Maxwellians
• Global Mild Solutions of the Landau and <scp>Non‐Cutoff</scp> Boltzmann Equations
• Hypocoercivity for linear kinetic equations conserving mass
• Almost Exponential Decay Near Maxwellian
• Quantitative perturbative study of convergence to equilibrium for collisional kinetic models in the torus
• Problèmes aux limites pour les équations aux dérivées partielles du premier ordre à coefficients réels; théorèmes d'approximation; application à l'équation de transport
• On the initial boundary value problem for the Vlasov-Poisson-Boltzmann system
• Weak Poincaré inequalities and \(L^2\)-convergence rates of Markov semigroups

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