Strong L1convergence to equilibrium without entropy conditions for the boltzmann equation

DOI10.1080/03605309908821472zbMath1059.35014OpenAlexW2051589524MaRDI QIDQ4261552

Fredrik Abrahamsson

Publication date: 1999

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03605309908821472

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Integro-partial differential equations (45K05) Rarefied gas flows, Boltzmann equation in fluid mechanics (76P05) Kinetic theory of gases in time-dependent statistical mechanics (82C40) Partial differential equations of mathematical physics and other areas of application (35Q99)

Related Items (8)

Global existence of solutions of the Boltzmann equation for Bose-Einstein particles with anisotropic initial data ⋮ Stability, convergence to self-similarity and elastic limit for the Boltzmann equation for inelastic hard spheres ⋮ Cooling process for inelastic Boltzmann equations for hard spheres. II: Self-similar solutions and tail behavior ⋮ Mathematical treatment of the homogeneous Boltzmann equation for Maxwellian molecules in the presence of singular kernels ⋮ On backward solutions of the spatially homogeneous Boltzmann equation for Maxwelian molecules ⋮ Gaussian Lower Bounds for the Boltzmann Equation without Cutoff ⋮ Regularity theory for the spatially homogeneous Boltzmann equation with cut-off ⋮ On measure solutions of the Boltzmann equation. II: Rate of convergence to equilibrium

Cites Work

• \(L^ p\)-estimates for the nonlinear spatially homogeneous Boltzmann equation
• Stability in \(L^ 1\) for the spatially homogeneous Boltzmann equation
• Global boundedness of moments of solutions of the Boltzmann equation for forces of infinite range
• Strict entropy production bounds and stability of the rate of convergence to equilibrium for the Boltzmann equation
• A proof of the smoothing properties of the positive part of Boltzmann's kernel
• On the spatially homogeneous Boltzmann equation
• Sur la théorie de l'équation intégrodifferentielle de Boltzmann
• Entropy production estimates for Boltzmann equations with physically realistic collision kernels
• A Maxwellian lower bound for solutions to the Boltzmann equation
• Regularity in the boltzmann equation and the radon transform
• Stability and exponential convergence in Lp for the spatially homogeneous Boltzmann equation

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