Kinetic Schauder estimates with time-irregular coefficients and uniqueness for the Landau equation

DOI10.3934/dcds.2023137arXiv2205.12930OpenAlexW4388951745MaRDI QIDQ6195936

No author found.

Publication date: 14 March 2024

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2205.12930

zbMATH Keywords

fundamental solutionLandau equationSchauder estimatesKinetic Fokker-Planck equation

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Rarefied gas flows, Boltzmann equation in fluid mechanics (76P05) Gas dynamics (general theory) (76N15) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Kinetic theory of gases in time-dependent statistical mechanics (82C40) Weak solutions to PDEs (35D30) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Strong solutions to PDEs (35D35) Boltzmann equations (35Q20) Fokker-Planck equations (35Q84) PDEs in connection with statistical mechanics (35Q82) Classical solutions to PDEs (35A09)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• A non-local inequality and global existence
• Uniqueness of solutions for the non-cutoff Boltzmann equation with soft potential
• Estimates for radial solutions of the homogeneous Landau equation with Coulomb potential
• Bounded solutions of the Boltzmann equation in the whole space
• The \(C^{\alpha}\) regularity of weak solutions of ultraparabolic equations
• Uniqueness of bounded solutions for the homogeneous Landau equation with a Coulomb potential
• Regularizing effect and local existence for the non-cutoff Boltzmann equation
• Upper bounds for parabolic equations and the Landau equation
• Schauder estimates for nonlocal kinetic equations and applications
• Blow up and regularity for fractal Burgers equation
• Schauder estimates for parabolic nondivergence operators of Hörmander type
• Schauder estimates, Harnack inequality and Gaussian lower bound for Kolmogorov-type operators in non-divergence form
• The Euler equations as a differential inclusion
• Well-posedness of the spatially homogeneous Landau equation for soft potentials
• The \(C^{\alpha}\) regularity of a class of non-homogeneous ultraparabolic equations
• Regularity of the moments of the solution of a transport equation
• Parabolic interior Schauder estimates by the maximum principle
• Intermediate Schauder theory for second order parabolic equations. IV: Time irregularity and regularity
• Hypoelliptic regularity in kinetic equations.
• The Dirichlet problem for a class of ultraparabolic equations
• Local existence, lower mass bounds, and a new continuation criterion for the Landau equation
• Dini and Schauder estimates for nonlocal fully nonlinear parabolic equations with drifts
• Global a priori estimates for the inhomogeneous Landau equation with moderately soft potentials
• Nonuniqueness of weak solutions to the Navier-Stokes equation
• Zufällige Bewegungen. (Zur Theorie der Brownschen Bewegung.)
• The Landau equation in a periodic box
• On the Cauchy problem for Landau equations: Sequential stability, global existence
• The Schauder estimate for kinetic integral equations
• Kinetic maximal \(L^p\)-regularity with temporal weights and application to quasilinear kinetic diffusion equations
• The Schauder estimate in kinetic theory with application to a toy nonlinear model
• Fundamental solutions for Kolmogorov-Fokker-Planck operators with time-depending measurable coefficients
• Global \({L}_p\) estimates for kinetic Kolmogorov-Fokker-Planck equations in nondivergence form
• Quantitative De Giorgi methods in kinetic theory
• Local solutions of the Landau equation with rough, slowly decaying initial data
• Global in time estimates for the spatially homogeneous Landau equation with soft potentials
• \(C^\infty\) smoothing for weak solutions of the inhomogeneous Landau equation
• A review for an isotropic Landau model
• Local existence with mild regularity for the Boltzmann equation
• Some a priori estimates for the homogeneous Landau equation with soft potentials
• Hypoelliptic second order differential equations
• Interior Schauder estimates for parabolic differential- (or difference-) equations via the maximum principle
• Regularity for the Boltzmann equation conditional to macroscopic bounds
• The Vlasov-Poisson-Landau system in a periodic box
• Hypocoercivity
• On the solutions of the first boundary value problem for the linear parabolic equations
• Global Existence of Weak Even Solutions for an Isotropic Landau Equation with Coulomb Potential
• Harnack inequality for kinetic Fokker-Planck equations with rough coefficients and application to the Landau equation
• On the spatially homogeneous landau equation for hard potentials part i : existence, uniqueness and smoothness
• On the spatially homogeneous landau equation for hard potentials part ii : h-theorem and applications
• Velocity Averaging and Hölder Regularity for Kinetic Fokker--Planck Equations with General Transport Operators and Rough Coefficients
• Global Mild Solutions of the Landau and <scp>Non‐Cutoff</scp> Boltzmann Equations
• DE GIORGI–NASH–MOSER AND HÖRMANDER THEORIES: NEW INTERPLAYS
• Partial Schauder Estimates for Second-Order Elliptic and Parabolic Equations: A Revisit
• Quantitative perturbative study of convergence to equilibrium for collisional kinetic models in the torus
• The Fundamental Solution of a Degenerate Partial Differential Equation of Parabolic Type

This page was built for publication: Kinetic Schauder estimates with time-irregular coefficients and uniqueness for the Landau equation