Spectral gap and coercivity estimates for linearized Boltzmann collision operators without angular cutoff

DOI10.1016/j.matpur.2007.03.003zbMath1388.76338arXivmath/0607495OpenAlexW2063541189MaRDI QIDQ884004

Clément Mouhot, Robert M. Strain

Publication date: 13 June 2007

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0607495

zbMATH Keywords

spectral gapBoltzmann operatorlong-range interactionsoft potentialsLandau operator

Mathematics Subject Classification ID

Rarefied gas flows, Boltzmann equation in fluid mechanics (76P05) Kinetic theory of gases in time-dependent statistical mechanics (82C40) Statistical mechanics of gases (82D05) Kinetic theory of gases in equilibrium statistical mechanics (82B40)

Related Items

Cauchy problem and exponential stability for the inhomogeneous Landau equation ⋮ Regularization estimates and hydrodynamical limit for the Landau equation ⋮ Convergence to equilibrium of some kinetic models ⋮ Propagation of Gevrey regularity for solution of non-cutoff Boltzmann equation ⋮ Singular behavior of the macroscopic quantity near the boundary for a Lorentz-gas model with the infinite-range potential ⋮ Global existence of non-cutoff Boltzmann equation in weighted Sobolev space ⋮ Spectrum analysis of some kinetic equations ⋮ Landau equation for very soft and Coulomb potentials near maxwellians ⋮ The Boltzmann equation without angular cutoff ⋮ Spectral gap and exponential convergence to equilibrium for a multi-species Landau system ⋮ The Vlasov-Poisson-Boltzmann system without angular cutoff ⋮ Spectral and phase space analysis of the linearized non-cutoff Kac collision operator ⋮ Exponential convergence to equilibrium for the homogeneous Landau equation with hard potentials ⋮ Compactness property of the linearized Boltzmann operator for a polyatomic gas undergoing resonant collisions ⋮ Global hypoelliptic and symbolic estimates for the linearized Boltzmann operator without angular cutoff ⋮ Regularization estimates and Cauchy theory for inhomogeneous Boltzmann equation for hard potentials without cut-off ⋮ An explicit coercivity estimate of the linearized quantum Boltzmann operator without angular cutoff ⋮ Fractional Poincaré inequalities for general measures ⋮ Spectrum structure and decay rate estimates on the Landau equation with Coulomb potential ⋮ The grazing collisions limit from the linearized Boltzmann equation to the Landau equation for short-range potentials ⋮ From Boltzmann's equation to the incompressible Navier-Stokes-Fourier system with long-range interactions ⋮ Regularized 13-moment equations for inverse power law models ⋮ Spectral gap formation to kinetic equations with soft potentials in bounded domain ⋮ 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 Vlasov–Poisson–Boltzmann/Landau System with Polynomial Perturbation Near Maxwellian ⋮ The smoothing effect in sharp Gevrey space for the spatially homogeneous non-cutoff Boltzmann equations with a hard potential ⋮ Global Regularity of the Vlasov-Poisson-Boltzmann System Near Maxwellian Without Angular Cutoff for Soft Potential ⋮ Solutions to the non-cutoff Boltzmann equation in the grazing limit ⋮ Propagation of Moments and Sharp Convergence Rate for Inhomogeneous Noncutoff Boltzmann Equation with Soft Potentials ⋮ Asymptotic analysis of the linearized Boltzmann collision operator from angular cutoff to non-cutoff ⋮ Spectral properties of the linearized Boltzmann operator in \(L^p\) for \(1\leq p\leq\infty\) ⋮ The Boltzmann equation, Besov spaces, and optimal time decay rates in \(\mathbb{R}_x^n\) ⋮ Hypoelliptic Estimates for a Linear Model of the Boltzmann Equation Without Angular Cutoff ⋮ Exponential convergence to equilibrium for the homogeneous Boltzmann equation for hard potentials without cut-off ⋮ The Boltzmann equation without angular cutoff in the whole space. I: global existence for soft potential ⋮ On exponential moments of the homogeneous Boltzmann equation for hard potentials without cutoff ⋮ From the Boltzmann equation to the incompressible Navier-Stokes equations on the torus: a quantitative error estimate ⋮ THE BOLTZMANN EQUATION WITHOUT ANGULAR CUTOFF IN THE WHOLE SPACE: II, GLOBAL EXISTENCE FOR HARD POTENTIAL ⋮ Global classical solutions of the Boltzmann equation without angular cut-off ⋮ Integral representation of the linear Boltzmann operator for granular gas dynamics with applications ⋮ Regularity of the Vlasov-Poisson-Boltzmann system without angular cutoff ⋮ A revisiting of the \(L^2\)-stability theory of the Boltzmann equation near global Maxwellians ⋮ On the rate of convergence to equilibrium for the linear Boltzmann equation with soft potentials ⋮ Non-cutoff Boltzmann equation with polynomial decay perturbations ⋮ Global hypoelliptic estimates for fractional order kinetic equation ⋮ Anisotropic hypoelliptic estimates for Landau-type operators ⋮ Well-posedness of spatially homogeneous Boltzmann equation with full-range interaction ⋮ Global existence and full regularity of the Boltzmann equation without angular cutoff ⋮ Exponential convergence for the linear homogeneous Boltzmann equation for hard potentials ⋮ Sharp anisotropic estimates for the Boltzmann collision operator and its entropy production ⋮ Hypocoercivity for a Linearized Multispecies Boltzmann System ⋮ Regularizing effect and local existence for the non-cutoff Boltzmann equation ⋮ Unnamed Item ⋮ Global classical solutions of the Boltzmann equation with long-range interactions ⋮ Long-time behaviour for the Landau equation ⋮ Stability of the spectral gap for the Boltzmann multi-species operator linearized around non-equilibrium Maxwell distributions ⋮ Incompressible Navier-Stokes-Fourier limit from the Landau equation ⋮ Compactness of Linearized Kinetic Operators ⋮ Explicit Coercivity Estimates for the Linearized Boltzmann and Landau Operators ⋮ Asymptotic stability of the relativistic Boltzmann equation without angular cut-off ⋮ Long-time asymptotics for homoenergetic solutions of the Boltzmann equation: collision-dominated case ⋮ Regularity of Non-cutoff Boltzmann Equation with Hard Potential ⋮ On the rate of convergence to equilibrium for the homogeneous Landau equation with soft potentials ⋮ Hermite basis diagonalization for the non-cutoff radially symmetric linearized Boltzmann operator ⋮ The Gevrey smoothing effect for the spatially inhomogeneous Boltzmann equations without cut-off

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the Cauchy problem of the Boltzmann equation with a soft potential
• Intermolecular forces of infinite range and the Boltzmann equation
• Stability of the relativistic Maxwellian in a collisional plasma
• Rate of convergence to equilibrium for the spatially homogeneous Boltzmann equation with hard potentials
• On the Cauchy problem for Boltzmann equations: Global existence and weak stability
• The Vlasov-Maxwell-Boltzmann system in the whole space
• Asymptotic behaviour of the Boltzmann equation with infinite range forces
• Regularity estimates via the entropy dissipation for the spatially homogeneous Boltzmann equation without cut-off
• The Boltzmann equation with a soft potential. I: Linear, spatially- homogeneous
• Global boundedness of moments of solutions of the Boltzmann equation for forces of infinite range
• The Boltzmann equation and its applications
• On a new class of weak solutions to the spatially homogeneous Boltzmann and Landau equations
• On Boltzmann equations and Fokker-Planck asymptotics: Influence of grazing collisions
• The mathematical theory of dilute gases
• Dispersion relations for the linearized Fokker-Planck equation
• The Vlasov-Maxwell-Boltzmann system near Maxwellians
• Classical solutions to the Boltzmann equation for molecules with an angular cutoff
• On the Landau approximation in plasma physics.
• Entropy dissipation and long-range interactions
• On the rate of entropy production for the Boltzmann equation
• The Landau equation in a periodic box
• Cercignani's conjecture is sometimes true and always almost true
• About the regularizing properties of the non-cut-off Kac equation
• Exponential decay for soft potentials near Maxwellian
• Explicit spectral gap estimates for the linearized Boltzmann and Landau operators with hard potentials
• Regularization for the non-cutoff 2D radially symmetric boltzmann equation with a velocity dependent cross section
• On asymptotics of the Boltzmann equation when the collisions become grazing
• THE FOKKER-PLANCK ASYMPTOTICS OF THE BOLTZMANN COLLISION OPERATOR IN THE COULOMB CASE
• Boltzmann collision operator with inverse‐power intermolecular potentials, I
• Régularité et compacité pour des noyaux de collision de Boltzmann sans troncature angulaire
• Une définition des solutions renormalisées pour l'équation de Boltzmann sans troncature angulaire
• Regularization properties of the 2-dimensional non radially symmetric non cutoff spatially homogeneous Boltzmann equation for Maxwellian molecules
• Around 3D Boltzmann non linear operator without angular cutoff, a new formulation
• Remarks on 3D Boltzmann linear equation without cutoff
• On the Boltzmann equation for long-range interactions
• The Vlasov‐Poisson‐Boltzmann system near Maxwellians
• The Boltzmann equation in the whole space
• On the spatially homogeneous landau equation for hard potentials part ii : h-theorem and applications
• Almost Exponential Decay Near Maxwellian
• LITTLEWOOD–PALEY THEORY AND REGULARITY ISSUES IN BOLTZMANN HOMOGENEOUS EQUATIONS I: NON-CUTOFF CASE AND MAXWELLIAN MOLECULES
• Quantitative perturbative study of convergence to equilibrium for collisional kinetic models in the torus
• Explicit Coercivity Estimates for the Linearized Boltzmann and Landau Operators
• ON THE CONNECTION BETWEEN A SOLUTION OF THE BOLTZMANN EQUATION AND A SOLUTION OF THE LANDAU-FOKKER-PLANCK EQUATION