Regularity estimates and open problems in kinetic equations

DOI10.1007/978-3-031-34089-5_3arXiv2204.06401MaRDI QIDQ6191311

No author found.

Publication date: 7 March 2024

Published in: A³N²M: Approximation, Applications, and Analysis of Nonlocal, Nonlinear Models (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2204.06401

zbMATH Keywords

long-range interactions kinetic equations Landau equation conditional regularity a non-cutoff Boltzmann equation

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Rarefied gas flows, Boltzmann equation in fluid mechanics (76P05) A priori estimates in context of PDEs (35B45) Boltzmann equations (35Q20)

Cites Work

Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Schauder estimates for solutions of linear parabolic integro-differential equations
BV-regularity of the Boltzmann equation in non-convex domains
Regularity for parabolic integro-differential equations with very irregular kernels
A new regularization mechanism for the Boltzmann equation without cut-off
A non-local inequality and global existence
Non-local gradient dependent operators
Smoothing effect of weak solutions for the spatially homogeneous Boltzmann equation without angular cutoff
Regularity for fully nonlinear nonlocal parabolic equations with rough kernels
Regularity of the Boltzmann equation in convex domains
Estimates for radial solutions of the homogeneous Landau equation with Coulomb potential
Intrinsic scaling properties for nonlocal operators
Gevrey smoothing effect of solutions for spatially homogeneous nonlinear Boltzmann equation without angular cutoff
On the differentiability of the solution to the Hamilton-Jacobi equation with critical fractional diffusion
The \(C^{\alpha}\) regularity of weak solutions of ultraparabolic equations
Formation and propagation of discontinuity for Boltzmann equation in non-convex domains
The Boltzmann equation without angular cutoff in the whole space. I: global existence for soft potential
Well-posedness of spatially homogeneous Boltzmann equation with full-range interaction
Smoothing estimates for Boltzmann equation with full-range interactions: spatially homogeneous case
The Boltzmann equation without angular cutoff in the whole space: qualitative properties of solutions
Decay and continuity of the Boltzmann equation in bounded domains
An integro-differential equation without continuous solutions
Upper bounds for parabolic equations and the Landau equation
Stability and uniqueness for the spatially homogeneous Boltzmann equation with long-range interactions
On the Cauchy problem for Boltzmann equations: Global existence and weak stability
A priori estimates for integro-differential operators with measurable kernels
Regularity of solutions for spatially homogeneous Boltzmann equation without angular cutoff
Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation
Littlewood-Paley theory and regularity issues in Boltzmann homogeneous equations. II. Non cutoff case and non Maxwellian molecules
Regularity of solutions to the spatially homogeneous Boltzmann equation without angular cutoff
Upper Maxwellian bounds for the spatially homogeneous Boltzmann equation
The \(C^{\alpha}\) regularity of a class of non-homogeneous ultraparabolic equations
Harnack inequality for some classes of Markov processes
Entropy dissipation and long-range interactions
Harnack inequalities for jump processes
Local existence, lower mass bounds, and a new continuation criterion for the Landau equation
On \(A_p\) weights and 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
On the trend to global equilibrium for spatially inhomogeneous kinetic systems: the Boltzmann equation
Uniform estimates for fundamental solutions associated with nonlocal Dirichlet forms
Regularity for solutions of nonlocal, nonsymmetric equations
The Landau equation with the specular reflection boundary condition
Non-cutoff Boltzmann equation with polynomial decay perturbations
The Schauder estimate for kinetic integral equations
On blow up for the energy super critical defocusing nonlinear Schrödinger equations
Stability of vacuum for the Boltzmann equation with moderately soft potentials
On the implosion of a compressible fluid. II: Singularity formation
Regularization estimates and Cauchy theory for inhomogeneous Boltzmann equation for hard potentials without cut-off
Coercivity estimates for integro-differential operators
Local well-posedness of the Boltzmann equation with polynomially decaying initial data
Self-generating lower bounds and continuation for the Boltzmann equation
On the Cauchy problem for integro-differential operators in Hölder classes and the uniqueness of the martingale problem
Stability of vacuum for the Landau equation with moderately soft potentials
The weak Harnack inequality for the Boltzmann equation without cut-off
\(C^\infty\) smoothing for weak solutions of the inhomogeneous Landau equation
Decay estimates for large velocities in the Boltzmann equation without cutoff
Local existence with mild regularity for the Boltzmann equation
Regularity for solutions of non local parabolic equations
Regularity for the Boltzmann equation conditional to macroscopic bounds
De Giorgi argument for weighted \(L^2\cap L^{\infty}\) solutions to the non-cutoff Boltzmann equation
Transition Probabilities for Symmetric Jump Processes
Local Regularity for Parabolic Nonlocal Operators
Global Solutions to a Non-Local Diffusion Equation with Quadratic Non-Linearity
Integro-Differential equations with nonlinear directional dependence
Local existence of polynomial decay solutions to the Boltzmann equation for soft potentials
THE BOLTZMANN EQUATION WITHOUT ANGULAR CUTOFF IN THE WHOLE SPACE: II, GLOBAL EXISTENCE FOR HARD POTENTIAL
Global classical solutions of the Boltzmann equation without angular cut-off
Regularity theory for parabolic nonlinear integral operators
Smoothness of the Solution of the Spatially Homogeneous Boltzmann Equation without Cutoff
Gaussian Lower Bounds for the Boltzmann Equation without Cutoff
Non-local Dirichlet forms and symmetric jump processes
Regularity theory for fully nonlinear integro-differential equations
ON THE SPATIALLY HOMOGENEOUS LANDAU EQUATION FOR MAXWELLIAN MOLECULES
Regularization properties of the 2-dimensional non radially symmetric non cutoff spatially homogeneous Boltzmann equation for Maxwellian molecules
Schauder estimates for an integro-differential equation with applications to a nonlocal Burgers equation
The Boltzmann Equation with Specular Boundary Condition in Convex Domains
Harnack inequality for kinetic Fokker-Planck equations with rough coefficients and application to the Landau equation
On the Boltzmann equation for long-range interactions
Harnack inequalities for non-local operators of variable order
On the spatially homogeneous landau equation for hard potentials part i : existence, uniqueness and smoothness
Global Mild Solutions of the Landau and <scp>Non‐Cutoff</scp> Boltzmann Equations
Partial Regularity in Time for the Space-Homogeneous Landau equation with Coulomb Potential
On Pointwise Exponentially Weighted Estimates for the Boltzmann Equation
Regularity results for nonlocal parabolic equations
THE MOSER'S ITERATIVE METHOD FOR A CLASS OF ULTRAPARABOLIC EQUATIONS
LITTLEWOOD–PALEY THEORY AND REGULARITY ISSUES IN BOLTZMANN HOMOGENEOUS EQUATIONS I: NON-CUTOFF CASE AND MAXWELLIAN MOLECULES
Emergence of exponentially weighted L^p-norms and Sobolev regularity for the Boltzmann equation
Holder estimates for solutions of integro differential equations like the fractional laplace
Hölder Continuity of Harmonic Functions with Respect to Operators of Variable Order
Global regularity estimates for the Boltzmann equation without cut-off

This page was built for publication: Regularity estimates and open problems in kinetic equations