Regularity of solutions for the Boltzmann equation without angular cutoff

DOI10.1016/j.crma.2009.04.025zbMath1167.35322OpenAlexW1993843093MaRDI QIDQ1028077

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

Publication date: 30 June 2009

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.crma.2009.04.025

zbMATH Keywords

generalized uncertainty principlecoercivity estimatesnonlinear collision operator

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Rarefied gas flows, Boltzmann equation in fluid mechanics (76P05)

Related Items (7)

Local existence, lower mass bounds, and a new continuation criterion for the Landau equation ⋮ A new regularization mechanism for the Boltzmann equation without cut-off ⋮ Global classical solutions of the Boltzmann equation without angular cut-off ⋮ Global existence and full regularity of the Boltzmann equation without angular cutoff ⋮ Global well-posedness theory for the spatially inhomogeneous Boltzmann equation without angular cutoff ⋮ Existence of local solutions for the Boltzmann equation without angular cutoff ⋮ Global regularity estimates for the Boltzmann equation without cut-off

Cites Work

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• Smoothing effects for classical solutions of the full Landau equation
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• Uncertainty principle and kinetic equations
• The Boltzmann equation and its applications
• Entropy dissipation and long-range interactions
• On the singularities of the global small solutions of the full Boltzmann equation
• About the regularizing properties of the non-cut-off Kac equation
• 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 $0 less than u less than 1$
• Local solutions in gevrey classes to the nonlinear Boltzmann equation without cutoff
• Regularization properties of the 2-dimensional non radially symmetric non cutoff spatially homogeneous Boltzmann equation for Maxwellian molecules
• LITTLEWOOD–PALEY THEORY AND REGULARITY ISSUES IN BOLTZMANN HOMOGENEOUS EQUATIONS I: NON-CUTOFF CASE AND MAXWELLIAN MOLECULES
• Some solutions of the Boltzmann equation without angular cutoff.

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