Renormalized solutions of some transport equations with partially W 1,1 velocities and applications
Lions, Pierre-Louis; Le Bris, Claude (2004), Renormalized solutions of some transport equations with partially W 1,1 velocities and applications, Annali di Matematica Pura ed Applicata, 183, 1, p. 97-130. http://dx.doi.org/10.1007/s10231-003-0082-4
TypeArticle accepté pour publication ou publié
Journal nameAnnali di Matematica Pura ed Applicata
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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.
Subjects / Keywordsordinary differential equations; transport equations
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