Global existence and full regularity of the Boltzmann equation without angular cutoff

DOI10.1007/s00220-011-1242-9zbMath1230.35082arXiv0912.1426OpenAlexW1966956543MaRDI QIDQ543367

Chao-Jiang Xu, Tong Yang, Yoshinori Morimoto, Seiji Ukai, Radjesvarane Alexandre

Publication date: 17 June 2011

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0912.1426

zbMATH Keywords

Cauchy problemlocal existenceBoltzmann equationglobal existence

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Kinetic theory of gases in time-dependent statistical mechanics (82C40) Boltzmann equations (35Q20) Classical solutions to PDEs (35A09)

Related Items (66)

Stability of vacuum for the Boltzmann equation with moderately soft potentials ⋮ On uniqueness and stability for the Boltzmann-Enskog equation ⋮ Partial regularity up to the boundary for solutions of subquadratic elliptic systems ⋮ Global solutions in the critical Besov space for the non-cutoff Boltzmann equation ⋮ A new regularization mechanism for the Boltzmann equation without cut-off ⋮ 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 ⋮ Cutoff Boltzmann equation with polynomial perturbation near Maxwellian ⋮ Local Well-Posedness for the Boltzmann Equation with Very Soft Potential and Polynomially Decaying Initial Data ⋮ The Boltzmann equation without angular cutoff ⋮ Small data global well-posedness for a Boltzmann equation via bilinear spacetime estimates ⋮ The Vlasov-Poisson-Boltzmann system without angular cutoff ⋮ Boltzmann equation with cutoff Rutherford scattering cross section near Maxwellian ⋮ Spectral and phase space analysis of the linearized non-cutoff Kac collision operator ⋮ Global Solution for the Spatially Inhomogeneous Non-cutoff Kac Equation ⋮ Local existence of polynomial decay solutions to the Boltzmann equation for soft potentials ⋮ Local well-posedness for Boltzmann's equation and the Boltzmann hierarchy via Wigner transform ⋮ Regularization estimates and Cauchy theory for inhomogeneous Boltzmann equation for hard potentials without cut-off ⋮ Local Existence for the Landau Equation with Hard Potentials ⋮ De Giorgi argument for weighted \(L^2\cap L^{\infty}\) solutions to the non-cutoff Boltzmann equation ⋮ Analytic smoothing effect of the spatially inhomogeneous Landau equations for hard potentials ⋮ Noncutoff Boltzmann equation with soft potentials in the whole space ⋮ Spectrum structure and behavior of the Vlasov-Maxwell-Boltzmann system without angular cutoff ⋮ Global well-posedness of the quantum Boltzmann equation for bosons interacting via inverse power law potentials ⋮ An \(\boldsymbol{L^1_{k}\cap L^{p}_{k}}\) Approach for the Non-Cutoff Boltzmann Equation in \(\boldsymbol{\mathbb{R}^3}\) ⋮ Hypocoercivity for perturbation theory and perturbation of hypocoercivity for confined Boltzmann-type collisional equations ⋮ The Vlasov–Poisson–Landau system in the weakly collisional regime ⋮ Local well-posedness of the Boltzmann equation with polynomially decaying initial data ⋮ The Vlasov–Poisson–Boltzmann/Landau System with Polynomial Perturbation Near Maxwellian ⋮ Stability of vacuum for the Landau equation with hard potentials ⋮ Global Regularity of the Vlasov-Poisson-Boltzmann System Near Maxwellian Without Angular Cutoff for Soft Potential ⋮ Propagation of Moments and Sharp Convergence Rate for Inhomogeneous Noncutoff Boltzmann Equation with Soft Potentials ⋮ Global solutions and time decay of the non-cutoff Vlasov-Maxwell-Boltzmann system in the whole space ⋮ The Vlasov-Poisson-Boltzmann system with angular cutoff for soft potentials ⋮ Analytic smoothing effect for the nonlinear Landau equation of Maxwellian molecules ⋮ Incompressible Navier-Stokes-Fourier Limit from The Boltzmann Equation: Classical Solutions ⋮ The Vlasov-Poisson-Boltzmann system for non-cutoff hard potentials ⋮ Gaussian Lower Bounds for the Boltzmann Equation without Cutoff ⋮ The Boltzmann equation without angular cutoff in the whole space. I: global existence for soft potential ⋮ The Cauchy problem for the inhomogeneous non-cutoff Kac equation in critical Besov space ⋮ Regularity of the Vlasov-Poisson-Boltzmann system without angular cutoff ⋮ From Newton's law to the linear Boltzmann equation without cut-off ⋮ Asymptotic analysis of the spatially homogeneous Boltzmann equation: grazing collisions limit ⋮ Non-cutoff Boltzmann equation with polynomial decay perturbations ⋮ Uncertainty principle and kinetic equations ⋮ Well-posedness of spatially homogeneous Boltzmann equation with full-range interaction ⋮ Sharp anisotropic estimates for the Boltzmann collision operator and its entropy production ⋮ The Boltzmann equation with frictional force for soft potentials in the whole space ⋮ Smoothing estimates for Boltzmann equation with full-range interactions: spatially homogeneous case ⋮ The Boltzmann equation without angular cutoff in the whole space: qualitative properties of solutions ⋮ Smoothing estimates for Boltzmann equation with full-range interactions: spatially inhomogeneous case ⋮ Stability of vacuum for the Landau equation with moderately soft potentials ⋮ Global well-posedness theory for the spatially inhomogeneous Boltzmann equation without angular cutoff ⋮ On the determinant problem for the relativistic Boltzmann equation ⋮ Hypocoercivity Based Sensitivity Analysis and Spectral Convergence of the Stochastic Galerkin Approximation to Collisional Kinetic Equations with Multiple Scales and Random Inputs ⋮ Hypoelliptic estimates in radiative transfer ⋮ The incompressible Navier-Stokes-Fourier limit from Boltzmann-Fermi-Dirac equation ⋮ Global existence and time decay of the non-cutoff Boltzmann equation with hard potential ⋮ Gevrey regularity of mild solutions to the non-cutoff Boltzmann equation ⋮ Gelfand-Shilov and Gevrey smoothing effect of the Cauchy problem for Fokker-Planck equation ⋮ \(L^2\) solution of linear non-cutoff Boltzmann equation with boundary conditions ⋮ The Enskog process for hard and soft potentials ⋮ Asymptotic stability of the relativistic Boltzmann equation without angular cut-off ⋮ Regularity of Non-cutoff Boltzmann Equation with Hard Potential ⋮ Gelfand-Shilov and Gevrey smoothing effect for the spatially inhomogeneous non-cutoff Kac equation ⋮ Hermite basis diagonalization for the non-cutoff radially symmetric linearized Boltzmann operator

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Energy method for Boltzmann equation
• Gevrey smoothing effect of solutions for spatially homogeneous nonlinear Boltzmann equation without angular cutoff
• The Boltzmann equation without angular cutoff in the whole space. I: global existence for soft potential
• The Boltzmann equation without angular cutoff in the whole space: qualitative properties of solutions
• Regularizing effect and local existence for the non-cutoff Boltzmann equation
• Intermolecular forces of infinite range and the Boltzmann equation
• Smoothing effects for classical solutions of the full Landau equation
• Stability of the Boltzmann equation with potential forces on torus
• 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
• Regularity of solutions for spatially homogeneous Boltzmann equation without angular cutoff
• Uncertainty principle and kinetic equations
• A review of Boltzmann equation with singular kernels
• The Vlasov-Maxwell-Boltzmann system in the whole space
• Regularity of solutions to the spatially homogeneous Boltzmann equation without angular cutoff
• Regularity of solutions for the Boltzmann equation without angular cutoff
• Existence of local solutions for the Boltzmann equation without angular cutoff
• A combination of energy method and spectral analysis for study of equations of gas motion
• The uncertainty principle and hypoelliptic operators
• Regularity estimates via the entropy dissipation for the spatially homogeneous Boltzmann equation without cut-off
• Estimates for degenerate Schrödinger operators and hypoellipticity for infinitely degenerate elliptic operators
• The Boltzmann equation and its applications
• The Boltzmann equation. I. Uniqueness and local existence
• A proof of the smoothing properties of the positive part of Boltzmann's kernel
• On a new class of weak solutions to the spatially homogeneous Boltzmann and Landau equations
• A direct method for the regularity of the gain term in the Boltzmann equation
• The mathematical theory of dilute gases
• Compactness in Boltzmann's equation via Fourier integral operators and applications. I, II
• The positivity of Schrödinger operators and the hypoellipticity of second order degenerate elliptic operators
• Boltzmann equation: micro-macro decompositions and positivity of shock profiles
• Entropy dissipation and long-range interactions
• On the singularities of the global small solutions of the full Boltzmann equation
• The Landau equation in a periodic box
• About the regularizing properties of the non-cut-off Kac equation
• Uncertainty principle and regularity for Boltzmann type equations
• Exponential decay for soft potentials near Maxwellian
• Hypoellipticity for a class of kinetic equations
• Nonlinear stability of rarefaction waves for the Boltzmann equation
• THE BOLTZMANN EQUATION WITHOUT ANGULAR CUTOFF IN THE WHOLE SPACE: II, GLOBAL EXISTENCE FOR HARD POTENTIAL
• The uncertainty principle
• Global classical solutions of the Boltzmann equation with long-range interactions
• Gevrey Hypoellipticity for a Class of Kinetic Equations
• Regularization for the non-cutoff 2D radially symmetric boltzmann equation with a velocity dependent cross section
• Smoothness of the Solution of the Spatially Homogeneous Boltzmann Equation without Cutoff
• Integral estimates for a linear singular operator linked with the Boltzmann operator: Part I: Small singularities $0 less than u less than 1$
• PROPAGATION OF SINGULARITIES IN THE SOLUTIONS TO THE BOLTZMANN EQUATION NEAR EQUILIBRIUM
• Convergence rate for the Boltzmann and Landau equations with soft potentials
• Propagation of Gevrey regularity for solutions of the Boltzmann equation for Maxwellian molecules
• Local solutions in gevrey classes to the nonlinear Boltzmann equation without cutoff
• Boltzmann collision operator with inverse‐power intermolecular potentials, I
• On the existence of global solutions of mixed problem for non-linear Boltzmann equation
• Régularité et compacité pour des noyaux de collision de Boltzmann sans troncature angulaire
• On Boltzmann and Landau equations
• 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 Boltzmann equation in the whole space
• On the spatially homogeneous landau equation for hard potentials part i : existence, uniqueness and smoothness
• LITTLEWOOD–PALEY THEORY AND REGULARITY ISSUES IN BOLTZMANN HOMOGENEOUS EQUATIONS I: NON-CUTOFF CASE AND MAXWELLIAN MOLECULES
• Explicit Coercivity Estimates for the Linearized Boltzmann and Landau Operators
• On a model Boltzmann equation without angular cutoff
• Some solutions of the Boltzmann equation without angular cutoff.

This page was built for publication: Global existence and full regularity of the Boltzmann equation without angular cutoff