Smoothing effect of weak solutions for the spatially homogeneous Boltzmann equation without angular cutoff

DOI10.1215/21562261-1625154zbMath1247.35085arXiv1104.5648OpenAlexW3102163166MaRDI QIDQ449150

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

Publication date: 12 September 2012

Published in: Kyoto Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1104.5648

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Weak solutions to PDEs (35D30) Boltzmann equations (35Q20)

Related Items (23)

About the Landau-Fermi-Dirac equation with moderately soft potentials ⋮ Global solutions in the critical Besov space for the non-cutoff Boltzmann equation ⋮ A new regularization mechanism for the Boltzmann equation without cut-off ⋮ Regularity for the Boltzmann equation conditional to macroscopic bounds ⋮ The Boltzmann equation without angular cutoff ⋮ Analytic smoothing effect of the spatially inhomogeneous Landau equations for hard potentials ⋮ High order approximation for the Boltzmann equation without angular cutoff under moderately soft potentials ⋮ Regularity estimates and open problems in kinetic equations ⋮ Gevrey regularity of spatially homogeneous Boltzmann equation without cutoff ⋮ On the emergence of quantum Boltzmann fluctuation dynamics near a Bose-Einstein condensate ⋮ High order approximation for the Boltzmann equation without angular cutoff ⋮ Emergence of exponentially weighted L^p-norms and Sobolev regularity for the Boltzmann equation ⋮ Gevrey regularity for the noncutoff nonlinear homogeneous Boltzmann equation with strong singularity ⋮ Measure valued solutions to the spatially homogeneous Boltzmann equation without angular cutoff ⋮ Asymptotic analysis of the spatially homogeneous Boltzmann equation: grazing collisions limit ⋮ Non-cutoff Boltzmann equation with polynomial decay perturbations ⋮ Gevrey smoothing for weak solutions of the fully nonlinear homogeneous Boltzmann and Kac equations without cutoff for Maxwellian molecules ⋮ The Boltzmann equation without angular cutoff in the whole space: qualitative properties of solutions ⋮ Macroscopic regularity for the Boltzmann equation ⋮ Entropy Dissipation Estimates for the Landau Equation: General Cross Sections ⋮ On Pointwise Exponentially Weighted Estimates for the Boltzmann Equation ⋮ Gelfand-Shilov and Gevrey smoothing effect for the spatially inhomogeneous non-cutoff Kac equation ⋮ Smoothing effect of the homogeneous Boltzmann equation with measure valued initial datum

Cites Work

• Bounded solutions of the Boltzmann equation in the whole space
• The Boltzmann equation without angular cutoff in the whole space. I: global existence for soft potential
• 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
• Regularizing effect and local existence for the non-cutoff Boltzmann equation
• Stability and uniqueness for the spatially homogeneous Boltzmann equation with long-range interactions
• Regularity of solutions for spatially homogeneous Boltzmann equation without angular cutoff
• 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
• On a new class of weak solutions to the spatially homogeneous Boltzmann and Landau equations
• Moment inequalities for the Boltzmann equation and applications to spatially homogneous problems
• Entropy dissipation and long-range interactions
• THE BOLTZMANN EQUATION WITHOUT ANGULAR CUTOFF IN THE WHOLE SPACE: II, GLOBAL EXISTENCE FOR HARD POTENTIAL
• Smoothness of the Solution of the Spatially Homogeneous Boltzmann Equation without Cutoff
• Local solutions in gevrey classes to the nonlinear Boltzmann equation without cutoff
• LITTLEWOOD–PALEY THEORY AND REGULARITY ISSUES IN BOLTZMANN HOMOGENEOUS EQUATIONS I: NON-CUTOFF CASE AND MAXWELLIAN MOLECULES
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