Optimality of integrability estimates for advection-diffusion equations

DOI10.1007/s00030-017-0455-9zbMath1373.35155arXiv1702.00321OpenAlexW2584849690MaRDI QIDQ2411100

Gianluca Crippa, Laura V. Spinolo, Stefano Bianchini, Maria Colombo

Publication date: 20 October 2017

Published in: NoDEA. Nonlinear Differential Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1702.00321

zbMATH Keywords

self-similar solutionsadvection-diffusion equationsparabolic equationsDuhamel formulaintegrability estimates and their optimality

Mathematics Subject Classification ID

A priori estimates in context of PDEs (35B45) PDEs with low regular coefficients and/or low regular data (35R05) Heat and other parabolic equation methods for PDEs on manifolds (58J35) Second-order parabolic equations (35K10)

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Maximal \(L^q\)-regularity for parabolic Hamilton-Jacobi equations and applications to mean field games ⋮ Existence and non-existence for time-dependent mean field games with strong aggregation ⋮ The Pontryagin maximum principle for solving Fokker-Planck optimal control problems ⋮ Error estimates for a finite volume scheme for advection–diffusion equations with rough coefficients ⋮ Lipschitz regularity for viscous Hamilton-Jacobi equations with \(L^p\) terms ⋮ Some fundamental a priori estimates for weak solutions of the evolution p-Laplacian equation ⋮ Non-uniqueness for the transport equation with Sobolev vector fields ⋮ A policy iteration method for mean field games ⋮ Transport equations with nonlocal diffusion and applications to Hamilton-Jacobi equations ⋮ Optimal stability estimates and a new uniqueness result for advection-diffusion equations

Cites Work

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• Finite time blowup for parabolic systems in two dimensions
• On the interior regularity of weak solutions of the Navier-Stokes equations
• Linear and quasilinear elliptic equations

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