An \(L^2\) to \(L^\infty\) framework for the Landau equation

DOI10.1007/s42543-019-00018-xzbMath1456.35196OpenAlexW3000374118WikidataQ126341739 ScholiaQ126341739MaRDI QIDQ827061

Yan Guo, Jinoh Kim, Hyung-Ju Hwang

Publication date: 6 January 2021

Published in: Peking Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s42543-019-00018-x

zbMATH Keywords

weak solutionexistence and uniquenessLandau equationHölder estimates\(L^{2}\) to \(L^{\infty }\) framework

Mathematics Subject Classification ID

Integro-partial differential equations (45K05) Nonlinear first-order PDEs (35F20) Theoretical approximation in context of PDEs (35A35) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Statistical mechanics of plasmas (82D10) Quantum hydrodynamics and relativistic hydrodynamics (76Y05) Weak solutions to PDEs (35D30) Integro-partial differential equations (35R09) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Boltzmann equations (35Q20) PDEs in connection with statistical mechanics (35Q82)

Related Items (21)

The initial boundary value problem for the Vlasov–Poisson–Fokker–Planck system ⋮ Global \({L}_p\) estimates for kinetic Kolmogorov-Fokker-Planck equations in nondivergence form ⋮ Asymptotics toward viscous contact waves for solutions of the Landau equation ⋮ Cutoff Boltzmann equation with polynomial perturbation near Maxwellian ⋮ Correction to: ``The Landau equation with the specular reflection boundary condition ⋮ On the quantum Boltzmann equation near Maxwellian and vacuum ⋮ De Giorgi argument for weighted \(L^2\cap L^{\infty}\) solutions to the non-cutoff Boltzmann equation ⋮ On \(C^2\) solution of the free-transport equation in a disk ⋮ Small Knudsen rate of convergence to contact wave for the Landau equation ⋮ Local-in-time strong solutions of the homogeneous Landau-Coulomb equation with \(L^p\) initial datum ⋮ An \(\boldsymbol{L^1_{k}\cap L^{p}_{k}}\) Approach for the Non-Cutoff Boltzmann Equation in \(\boldsymbol{\mathbb{R}^3}\) ⋮ Solutions to the non-cutoff Boltzmann equation uniformly near a Maxwellian ⋮ On a spatially inhomogeneous nonlinear Fokker-Planck equation: Cauchy problem and diffusion asymptotics ⋮ Global \(\boldsymbol{L}_{\boldsymbol{p}}\) Estimates for Kinetic Kolmogorov–Fokker–Planck Equations in Divergence Form ⋮ Compactness properties and local existence of weak solutions to the Landau equation ⋮ The Landau equation with the specular reflection boundary condition ⋮ Global strong solutions to the Vlasov-Poisson-Boltzmann system with soft potential in a bounded domain ⋮ Gevrey regularity of mild solutions to the non-cutoff Boltzmann equation ⋮ Kinetic Fokker-Planck and Landau equations with specular reflection boundary condition ⋮ The Vlasov-Poisson-Landau system with the specular-reflection boundary condition ⋮ The Navier-Stokes-Vlasov-Fokker-Planck system in bounded domains

Cites Work

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• Non-isothermal boundary in the Boltzmann theory and Fourier law
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• Sharp anisotropic estimates for the Boltzmann collision operator and its entropy production
• Decay and continuity of the Boltzmann equation in bounded domains
• The Fokker-Planck equation with absorbing boundary conditions
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• The Vlasov-Poisson-Landau system in \(\mathbb{R}^{3}_{x}\)
• On the kinetic Fokker-Planck equation in the half-space with absorbing barriers
• Global Solutions to a Non-Local Diffusion Equation with Quadratic Non-Linearity
• L 2-stability of the Landau equation near global Maxwellians
• Harnack inequality for kinetic Fokker-Planck equations with rough coefficients and application to the Landau equation
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• Pointwise Behavior of the Linearized Boltzmann Equation on a Torus

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