Local existence of polynomial decay solutions to the Boltzmann equation for soft potentials

DOI10.1142/S0219530514500079zbMath1326.35225OpenAlexW2170019161MaRDI QIDQ2947810

Yoshinori Morimoto, Tong Yang

Publication date: 29 September 2015

Published in: Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0219530514500079

zbMATH Keywords

local existenceBoltzmann equationnon-cutoff soft potential

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Rarefied gas flows, Boltzmann equation in fluid mechanics (76P05) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Kinetic theory of gases in equilibrium statistical mechanics (82B40) Boltzmann equations (35Q20)

Related Items (10)

Local Well-Posedness for the Boltzmann Equation with Very Soft Potential and Polynomially Decaying Initial Data ⋮ Regularity for the Boltzmann equation conditional to macroscopic bounds ⋮ On the cutoff approximation for the Boltzmann equation with long-range interaction ⋮ Local well-posedness of the Boltzmann equation with polynomially decaying initial data ⋮ Regularity estimates and open problems in kinetic equations ⋮ Solutions to the non-cutoff Boltzmann equation uniformly near a Maxwellian ⋮ Local solutions of the Landau equation with rough, slowly decaying initial data ⋮ Self-generating lower bounds and continuation for the Boltzmann equation ⋮ Decay estimates for large velocities in the Boltzmann equation without cutoff ⋮ Global regularity estimates for the Boltzmann equation without cut-off

Cites Work

• Uniqueness of solutions for the non-cutoff Boltzmann equation with soft potential
• Global existence and full regularity of the Boltzmann equation without angular cutoff
• Bounded solutions of the Boltzmann equation in the whole space
• The Boltzmann equation without angular cutoff in the whole space. I: global existence for soft potential
• The Boltzmann equation without angular cutoff in the whole space: qualitative properties of solutions
• Regularizing effect and local existence for the non-cutoff Boltzmann equation
• Uncertainty principle and kinetic equations
• Regularity of solutions to the spatially homogeneous Boltzmann equation without angular cutoff
• Entropy dissipation and long-range interactions

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