Partial Regularity in Time for the Space-Homogeneous Landau equation with Coulomb Potential

DOI10.24033/asens.2524zbMath1503.35123arXiv1906.02841OpenAlexW4287398579MaRDI QIDQ5056680

Cyril Imbert, Maria Pia Gualdani, François Golse, Alexis F. Vasseur

Publication date: 8 December 2022

Published in: Annales scientifiques de l'École Normale Supérieure (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1906.02841

zbMATH Keywords

partial regularityHausdorff dimensionCoulomb potentialLandau equationDe Giorgi method

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Nonlinear parabolic equations (35K55) Integro-partial differential equations (45K05) Weak solutions to PDEs (35D30) Blow-up in context of PDEs (35B44) Nonlinear initial, boundary and initial-boundary value problems for nonlinear parabolic equations (35K61) Integro-partial differential equations (35R09) Boltzmann equations (35Q20)

Related Items

Entropy dissipation estimates for the Boltzmann equation without cut-off, Well-posedness of the Lenard-Balescu equation with smooth interactions, Local-in-time strong solutions of the homogeneous Landau-Coulomb equation with \(L^p\) initial datum, Regularity estimates and open problems in kinetic equations, Stability of vacuum for the Landau equation with hard potentials, Radially symmetric models of the Landau kinetic equation and high energy tails

Cites Work

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• A non-local inequality and global existence
• Estimates for radial solutions of the homogeneous Landau equation with Coulomb potential
• Estimates for the large time behavior of the Landau equation in the Coulomb case
• Uniqueness of bounded solutions for the homogeneous Landau equation with a Coulomb potential
• Upper bounds for parabolic equations and the Landau equation
• Smoothing effects for classical solutions of the full Landau equation
• The Navier-Stokes equations on a bounded domain
• On a new class of weak solutions to the spatially homogeneous Boltzmann and Landau equations
• Local existence, lower mass bounds, and a new continuation criterion for the Landau equation
• On \(A_p\) weights and the Landau equation
• Landau equation for very soft and Coulomb potentials near maxwellians
• The Landau equation in a periodic box
• The weak Harnack inequality for the Boltzmann equation without cut-off
• \(C^\infty\) smoothing for weak solutions of the inhomogeneous Landau equation
• Entropy dissipation estimates for the Landau equation in the Coulomb case and applications
• An introduction to Navier-Stokes equation and oceanography.
• A new proof of partial regularity of solutions to Navier-Stokes equations
• Global Solutions to a Non-Local Diffusion Equation with Quadratic Non-Linearity
• On partial regularity results for the navier-stokes equations
• Fluid dynamic limits of kinetic equations II convergence proofs for the boltzmann equation
• On Boltzmann and Landau equations
• A new proof of the Caffarelli-Kohn-Nirenberg theorem
• Harnack inequality for kinetic Fokker-Planck equations with rough coefficients and application to the Landau equation
• Partial regularity of suitable weak solutions of the navier-stokes equations
• Well-Posedness and Asymptotics of Grazing Collisions Limit of Boltzmann Equation with Coulomb Interaction
• Regularity analysis for systems of reaction-diffusion equations