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Renormalized solutions of some transport equations with partially W 1,1 velocities and applications

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Date
2004
Dewey
Analyse
Sujet
ordinary differential equations; transport equations
Journal issue
Annali di Matematica Pura ed Applicata
Volume
183
Number
1
Publication date
2004
Article pages
97-130
Publisher
Springer
DOI
http://dx.doi.org/10.1007/s10231-003-0082-4
URI
https://basepub.dauphine.fr/handle/123456789/6033
Collections
  • CEREMADE : Publications
Metadata
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Author
Lions, Pierre-Louis
Le Bris, Claude
Type
Article accepté pour publication ou publié
Abstract (EN)
We prove existence and uniqueness of renormalized solutions of some transport equations with a vector field that is not W1,1 with respect to all variables but is of a particular form. Two specific applications of this new result are then treated, based upon the equivalence between transport equations and ordinary differential equations. The first one consists of a result about the dependance upon initial conditions for solutions of ODEs. The second one is related to some stochastic differential equations arising in the modelling of polymeric fluid flows.

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