Regularizing effect and local existence for the non-cutoff Boltzmann equation

DOI10.1007/s00205-010-0290-1zbMath1257.76099arXiv0909.1229OpenAlexW1978894893MaRDI QIDQ717165

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

Publication date: 27 September 2011

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0909.1229

zbMATH Keywords

coercivitycollision operatorhypo-ellipticitymild regularityupper bound estimates

Mathematics Subject Classification ID

Integro-partial differential equations (45K05) Rarefied gas flows, Boltzmann equation in fluid mechanics (76P05)

Related Items

Stability of vacuum for the Boltzmann equation with moderately soft potentials ⋮ Smoothing estimates of the Vlasov-Poisson-Landau system ⋮ Non-existence of some approximately self-similar singularities for the Landau, Vlasov-Poisson-Landau, and Boltzmann equations ⋮ Local existence, lower mass bounds, and a new continuation criterion for the Landau equation ⋮ Global solutions in the critical Besov space for the non-cutoff Boltzmann equation ⋮ FRACTIONAL ORDER KINETIC EQUATIONS AND HYPOELLIPTICITY ⋮ Propagation of Gevrey regularity for solution of 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 ⋮ Suppression of plasma echoes and Landau damping in Sobolev spaces by weak collisions in a Vlasov-Fokker-Planck equation ⋮ Cutoff Boltzmann equation with polynomial perturbation near Maxwellian ⋮ Local Well-Posedness for the Boltzmann Equation with Very Soft Potential and Polynomially Decaying Initial Data ⋮ Regularity for the Boltzmann equation conditional to macroscopic bounds ⋮ The Boltzmann equation without angular cutoff ⋮ Gevrey smoothing effect of solutions for spatially homogeneous nonlinear Boltzmann equation without angular cutoff ⋮ The Vlasov-Poisson-Boltzmann system without angular cutoff ⋮ Spectral and phase space analysis of the linearized non-cutoff Kac collision operator ⋮ Local existence of polynomial decay solutions to the Boltzmann equation for soft potentials ⋮ 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 ⋮ Vlasov-Poisson equation in weighted Sobolev space \(W^{m, p}(w)\) ⋮ 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 ⋮ On the Convergence from Boltzmann to Navier–Stokes–Fourier for General Initial Data ⋮ Analytic smoothing effect of the spatially inhomogeneous Landau equations for hard potentials ⋮ Noncutoff Boltzmann equation with soft potentials in the whole space ⋮ Local well-posedness of the Boltzmann equation with polynomially decaying initial data ⋮ 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 ⋮ Kinetic Schauder estimates with time-irregular coefficients and uniqueness for the Landau equation ⋮ 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 ⋮ Gevrey regularity of spatially homogeneous Boltzmann equation without cutoff ⋮ The Vlasov-Poisson-Boltzmann system with angular cutoff for soft potentials ⋮ Analytic smoothing effect for the nonlinear Landau equation of Maxwellian molecules ⋮ Gelfand-Shilov smoothing effect for the spatially inhomogeneous Boltzmann equations without cut-off ⋮ Sharp Regularizing Estimates for the Gain Term of the Boltzmann Collision Operator ⋮ Smoothing effect of weak solutions for the spatially homogeneous Boltzmann equation without angular cutoff ⋮ Local solutions of the Landau equation with rough, slowly decaying initial data ⋮ Emergence of exponentially weighted L^p-norms and Sobolev regularity for the Boltzmann equation ⋮ Smoothing properties of fractional Ornstein-Uhlenbeck semigroups and null-controllability ⋮ The Vlasov-Poisson-Boltzmann system for non-cutoff hard potentials ⋮ Hypoelliptic Estimates for a Linear Model of the Boltzmann Equation Without Angular Cutoff ⋮ The Boltzmann equation without angular cutoff in the whole space. I: global existence for soft potential ⋮ Regularizing effects for the classical solutions to the Landau equation in the whole space ⋮ 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 ⋮ The Cauchy problem for the inhomogeneous non-cutoff Kac equation in critical Besov space ⋮ Regularity of the Vlasov-Poisson-Boltzmann system without angular cutoff ⋮ A toy-model study of the grazing collisions in the kinetic theory ⋮ Enhanced dissipation, hypoellipticity, and anomalous small noise inviscid limits in shear flows ⋮ Asymptotic analysis of the spatially homogeneous Boltzmann equation: grazing collisions limit ⋮ Non-cutoff Boltzmann equation with polynomial decay perturbations ⋮ Gevrey regularity for solutions of the non-cutoff Boltzmann equation: the spatially inhomogeneous case ⋮ Global hypoelliptic estimates for fractional order kinetic equation ⋮ Well-posedness of spatially homogeneous Boltzmann equation with full-range interaction ⋮ Global existence and full regularity of the Boltzmann equation without angular cutoff ⋮ Sharp anisotropic estimates for the Boltzmann collision operator and its entropy production ⋮ Gevrey smoothing for weak solutions of the fully nonlinear homogeneous Boltzmann and Kac equations without cutoff for Maxwellian molecules ⋮ 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 ⋮ Hölder Continuity for a Family of Nonlocal Hypoelliptic Kinetic Equations ⋮ Macroscopic regularity for the Boltzmann equation ⋮ Regularity of solutions for the Boltzmann equation without angular cutoff ⋮ 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 ⋮ Boltzmann collision operator for the infinite range potential: a limit problem ⋮ Existence of local solutions for the Boltzmann equation without angular cutoff ⋮ Asymptotic stability of the relativistic Boltzmann equation without angular cut-off ⋮ Vlasov-Poisson equation in Besov space ⋮ Decay estimates for large velocities in the Boltzmann equation without cutoff ⋮ Regularity of Non-cutoff Boltzmann Equation with Hard Potential ⋮ Global regularity estimates for the Boltzmann equation without cut-off ⋮ Gelfand-Shilov and Gevrey smoothing effect for the spatially inhomogeneous non-cutoff Kac equation ⋮ The Gevrey smoothing effect for the spatially inhomogeneous Boltzmann equations without cut-off

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Intermolecular forces of infinite range and the Boltzmann equation
• Smoothing effects for classical solutions of the full Landau equation
• 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
• Smoothness of classical solutions to the Vlasov-Poisson-Landau system
• Regularity of solutions for spatially homogeneous Boltzmann equation without angular cutoff
• Uncertainty principle and kinetic equations
• Integral estimates for a linear singular operator linked with Boltzmann operators. II. High singularities \(1\leq\nu<2\)
• Littlewood-Paley theory and regularity issues in Boltzmann homogeneous equations. II. Non cutoff case and non Maxwellian molecules
• Regularity of solutions to the spatially homogeneous Boltzmann equation without angular cutoff
• Ultra-analytic effect of Cauchy problem for a class of kinetic equations
• The uncertainty principle and hypoelliptic operators
• Estimates for degenerate Schrödinger operators and hypoellipticity for infinitely degenerate elliptic operators
• The Boltzmann equation and its applications
• On a new class of weak solutions to the spatially homogeneous Boltzmann and Landau equations
• The mathematical theory of dilute gases
• The positivity of Schrödinger operators and the hypoellipticity of second order degenerate elliptic operators
• Hypoelliptic regularity in kinetic equations.
• On the Landau approximation in plasma physics.
• Entropy dissipation and long-range interactions
• 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
• Hypoellipticity for a class of kinetic equations
• The uncertainty principle
• 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
• 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
• Régularité et compacité pour des noyaux de collision 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
• On the Boltzmann equation for long-range interactions
• 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
• Asymptotic Theory of the Boltzmann Equation
• Some solutions of the Boltzmann equation without angular cutoff.