Optimality of integrability estimates for advection–diffusion equations

We discuss L p integrability estimates for the solution  u of the advection–diffusion equation  ∂ t u + div ( b u ) = Δ u , where the velocity field  b ∈ L t r L x q . We first summarize some classical results proving such estimates for certain ranges of the exponents r and q . Afterwards we prove t...

Full description

Saved in:
Bibliographic Details
Published in:Nonlinear differential equations and applications 2017-08, Vol.24 (4), Article 33
Main Authors: Bianchini, Stefano, Colombo, Maria, Crippa, Gianluca, Spinolo, Laura V.
Format: Article
Language:English
Subjects:
Advection
Analysis
Estimates
Exponents
Fluids
Hyperbolic PDEs
Mathematical analysis
Mathematics
Mathematics and Statistics
Optimization
Transport and Applications: Dedicated to Alberto Bressan for his 60th birthday
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We discuss L p integrability estimates for the solution  u of the advection–diffusion equation  ∂ t u + div ( b u ) = Δ u , where the velocity field  b ∈ L t r L x q . We first summarize some classical results proving such estimates for certain ranges of the exponents r and q . Afterwards we prove the optimality of such ranges by means of new original examples.
ISSN:1021-9722
1420-9004
DOI:10.1007/s00030-017-0455-9