Smooth solutions for the dyadic model

We consider the dyadic model, which is a toy model to test issues of well-posedness and blow-up for the Navier-Stokes and Euler equations. We prove well-posedness of positive solutions of the viscous problem in the relevant scaling range which corresponds to Navier-Stokes. Likewise we prove well-pos...

Full description

Saved in:
Bibliographic Details
Published in:Nonlinearity 2011-11, Vol.24 (11), p.3083-3097
Main Authors: Barbato, David, Morandin, Francesco, Romito, Marco
Format: Article
Language:English
Subjects:
Dyadics
Euler equations
Exact sciences and technology
Global analysis, analysis on manifolds
Mathematical analysis
Mathematical methods in physics
Mathematical models
Mathematics
Navier-Stokes equations
Nonlinearity
Numerical analysis
Numerical analysis. Scientific computation
Numerical linear algebra
Other topics in mathematical methods in physics
Partial differential equations
Physics
Regularity
Sciences and techniques of general use
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
Transport
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 consider the dyadic model, which is a toy model to test issues of well-posedness and blow-up for the Navier-Stokes and Euler equations. We prove well-posedness of positive solutions of the viscous problem in the relevant scaling range which corresponds to Navier-Stokes. Likewise we prove well-posedness for the inviscid problem (in a suitable regularity class) when the parameter corresponds to the strongest transport effect of the nonlinearity.
ISSN:0951-7715
1361-6544
DOI:10.1088/0951-7715/24/11/004