Dissipation and Semigroup on $H^k_n$: Non-cutoff Linearized Boltzmann Operator with Soft Potential

DOI10.1137/19M1263017zbMath1439.35596arXiv1905.07993OpenAlexW3038211345MaRDI QIDQ3296900

Dingqun Deng

Publication date: 2 July 2020

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1905.07993

zbMATH Keywords

strongly continuous semigroupdissipationBoltzmann equationpseudodifferential operatorlinearized collision operator

Mathematics Subject Classification ID

Pseudodifferential operators as generalizations of partial differential operators (35S05) One-parameter semigroups and linear evolution equations (47D06) Groups and semigroups of linear operators (47D03)

Related Items (9)

Smoothing estimates of the Vlasov-Poisson-Landau system ⋮ Low regularity solutions for the Vlasov–Poisson–Landau/Boltzmann system ⋮ Global existence of non-cutoff Boltzmann equation in weighted Sobolev space ⋮ Stability of rarefaction waves for the non-cutoff Vlasov-Poisson-Boltzmann system with physical boundary ⋮ Spectral gap formation to kinetic equations with soft potentials in bounded domain ⋮ The Vlasov–Poisson–Boltzmann/Landau System with Polynomial Perturbation Near Maxwellian ⋮ Global Regularity of the Vlasov-Poisson-Boltzmann System Near Maxwellian Without Angular Cutoff for Soft Potential ⋮ Regularity of the Vlasov-Poisson-Boltzmann system without angular cutoff ⋮ Regularity of Non-cutoff Boltzmann Equation with Hard Potential

Cites Work

• The Boltzmann equation without angular cutoff in the whole space. I: global existence for soft potential
• On the Cauchy problem of the Boltzmann equation with a soft potential
• Weighted distribution spaces and pseudodifferential operators
• The mathematical theory of dilute gases
• Entropy dissipation and long-range interactions
• Global hypoelliptic and symbolic estimates for the linearized Boltzmann operator without angular cutoff
• Global classical solutions of the Boltzmann equation without angular cut-off
• Espaces fonctionnels associés au calcul de Weyl-Hörmander
• On the Boltzmann equation for long-range interactions
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