Upper bounds for fundamental solutions to non-local diffusion equations with divergence free drift

DOI10.1016/j.jfa.2013.02.011zbMath1278.35262OpenAlexW2003583563MaRDI QIDQ387233

Hideyuki Miura, Yasunori Maekawa

Publication date: 20 December 2013

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jfa.2013.02.011

zbMATH Keywords

fundamental solutionsnon-local diffusiondivergence free driftpointwise upper bound

Mathematics Subject Classification ID

Fundamental solutions to PDEs (35A08) Fractional partial differential equations (35R11)

Related Items (13)

Heat kernels and analyticity of non-symmetric jump diffusion semigroups ⋮ Pointwise estimates for solutions of fractal Burgers equation ⋮ Fundamental solution of the fractional diffusion equation with a singular drift ⋮ Heat kernel for non-local operators with variable order ⋮ Heat kernel estimates for critical fractional diffusion operators ⋮ Fractional Kolmogorov operator and desingularizing weights ⋮ Upper heat kernel estimates for nonlocal operators via Aronson's method ⋮ Stable estimates for source solution of critical fractal Burgers equation ⋮ Uniform pointwise asymptotics of solutions to quasi-geostrophic equation ⋮ On fundamental solutions for non-local parabolic equations with divergence free drift ⋮ Osgood's lemma and some results for the slightly supercritical 2D Euler equations for incompressible flow ⋮ Green function for gradient perturbation of unimodal Lévy processes in the real line ⋮ Gevrey semigroup generated by \(- (\Lambda^\alpha + b \cdot \nabla)\) in \(L^p(\mathbb{R}^n)\)

Cites Work

• Unnamed Item
• Time-dependent gradient perturbations of fractional Laplacian
• On divergence-free drifts
• Dissipative quasi-geostrophic equation for large initial data in the critical Sobolev space
• Global well-posedness for the critical 2D dissipative quasi-geostrophic equation
• A lower bound for fundamental solutions of the heat convection equations
• Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation
• Symmetric jump processes: localization, heat kernels and convergence
• The Cauchy problem and the martingale problem for integro-differential operators with non-smooth kernels
• Regularity criteria for the dissipative quasi-geostrophic equations in Hölder spaces
• Upper bounds for symmetric Markov transition functions
• Diffusion processes with generators of generalized divergence form
• A strong regularity result for parabolic equations
• Harnack inequalities for jump processes
• On logarithmic Sobolev inequalities for higher order fractional derivatives
• A maximum principle applied to quasi-geostrophic equations
• Global well-posedness in the super-critical dissipative quasi-geostrophic equations
• Optimal smoothing and decay estimates for viscously damped conservation laws, with applications to the 2-D Navier-Stokes equation
• Variation on a theme of Caffarelli and Vasseur
• Estimates of heat kernel of fractional Laplacian perturbed by gradient operators
• On the theory of \({\mathcal L}_{p, \lambda}\) spaces
• On the critical dissipative quasi-geostrophic equation
• Heat kernel estimates for critical fractional diffusion operators
• Non-local Dirichlet forms and symmetric jump processes
• Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. (AM-105)
• Explicit Constants for Gaussian Upper Bounds on Heat Kernels
• Formation of strong fronts in the 2-D quasigeostrophic thermal active scalar

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