Probability Measures with Finite Moments and the Homogeneous Boltzmann Equation

DOI10.1137/15M105104XzbMath1347.35189MaRDI QIDQ5740327

Yoshinori Morimoto, Yong-Kum Cho, Shuaikun Wang, Tong Yang

Publication date: 26 July 2016

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

zbMATH Keywords

Fourier transformcharacteristic functionBoltzmann equationmomentprobability measuresymmetric difference operator

Mathematics Subject Classification ID

Rarefied gas flows, Boltzmann equation in fluid mechanics (76P05) Kinetic theory of gases in time-dependent statistical mechanics (82C40) Kinetic theory of gases in equilibrium statistical mechanics (82B40) Subelliptic equations (35H20) Boltzmann equations (35Q20) PDEs with measure (35R06)

Related Items (5)

Measure valued solution to the spatially homogeneous Boltzmann equation with inelastic long-range interactions ⋮ Smoothing effect and Cauchy problem for radially symmetric homogeneous Boltzmann equation with Debye-Yukawa potential of Shubin class initial datum ⋮ Cauchy Problem for the Spatially Homogeneous Landau Equation with Shubin Class Initial Datum and Gelfand--Shilov Smoothing Effect ⋮ The Cauchy problem for the radially symmetric homogeneous Boltzmann equation with Shubin class initial datum and Gelfand-Shilov smoothing effect ⋮ On the measure valued solution to the inelastic Boltzmann equation with soft potentials

Cites Work

• Regularity of solutions to the spatially homogeneous Boltzmann equation without angular cutoff
• Propagation of smoothness and the rate of exponential convergence to equilibrium for a spatially homogeneous Maxwellian gas
• On a class of characterization problems for random convex combinations
• Entropy dissipation and long-range interactions
• Metrics for probability distributions and the trend to equilibrium for solutions of the Boltzmann equation.
• Probability metrics and uniqueness of the solution to the Boltzmann equation for a Maxwell gas
• A remark on Cannone-Karch solutions to the homogeneous Boltzmann equation for Maxwellian molecules
• A new characterization and global regularity of infinite energy solutions to the homogeneous Boltzmann equation
• Smoothing effect of the homogeneous Boltzmann equation with measure valued initial datum
• Infinite energy solutions to the homogeneous Boltzmann equation
• Moment classification of infinite energy solutions to the homogeneous Boltzmann equation
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