Exponential convergence to equilibrium of solutions of the Kac equation and homogeneous Boltzmann equation for Maxwellian without angular cut-off

DOI10.3233/ASY-171407zbMath1367.35101OpenAlexW2588717324WikidataQ115488306 ScholiaQ115488306MaRDI QIDQ5347493

Fei Meng, Xiao-Ping Yang

Publication date: 24 May 2017

Published in: Asymptotic Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3233/asy-171407

zbMATH Keywords

Fourier transformBoltzmann equationKac equationMaxwelliannon-cut-off

Mathematics Subject Classification ID

PDEs with low regular coefficients and/or low regular data (35R05) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Boltzmann equations (35Q20)

Cites Work

• Unnamed Item
• The theory of the nonlinear Boltzmann equation for Maxwell molecules in Fourier representation
• Rate of convergence to equilibrium for the spatially homogeneous Boltzmann equation with hard potentials
• Decay rates in probability metrics towards homogeneous cooling states for the inelastic Maxwell model
• Regularity of solutions for spatially homogeneous Boltzmann equation without angular cutoff
• Regularity of solutions to the spatially homogeneous Boltzmann equation without angular cutoff
• Stability in \(L^ 1\) for the spatially homogeneous Boltzmann equation
• Strict entropy production bounds and stability of the rate of convergence to equilibrium for the Boltzmann equation
• Propagation of smoothness and the rate of exponential convergence to equilibrium for a spatially homogeneous Maxwellian gas
• Entropy dissipation and moment production for the Boltzmann equation
• Entropy dissipation and long-range interactions
• Metrics for probability distributions and the trend to equilibrium for solutions of the Boltzmann equation.
• Regularity theory for the spatially homogeneous Boltzmann equation with cut-off
• Sharp entropy dissipation bounds and explicit rate of trend to equilibrium for the spatially homogeneous Boltzmann equation
• On the rate of entropy production for the Boltzmann equation
• Probability metrics and uniqueness of the solution to the Boltzmann equation for a Maxwell gas
• Cercignani's conjecture is sometimes true and always almost true
• About the regularizing properties of the non-cut-off Kac equation
• Entropy production estimates for Boltzmann equations with physically realistic collision kernels
• Contractive metrics for a Boltzmann equation for granular gases: Diffusive equilibria
• Smoothness of the Solution of the Spatially Homogeneous Boltzmann Equation without Cutoff
• Propagation of Gevrey regularity for solutions of the Boltzmann equation for Maxwellian molecules
• Stability and exponential convergence in Lp for the spatially homogeneous Boltzmann equation
• LITTLEWOOD–PALEY THEORY AND REGULARITY ISSUES IN BOLTZMANN HOMOGENEOUS EQUATIONS I: NON-CUTOFF CASE AND MAXWELLIAN MOLECULES