Abstract
We prove existence and uniqueness of renormalized solutions of some transport equations with a vector field that is not W 1,1 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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Le Bris, C., Lions, PL. Renormalized solutions of some transport equations with partially W 1,1 velocities and applications. Ann. Mat. Pura Appl. IV. Ser. 183, 97–130 (2004). https://doi.org/10.1007/s10231-003-0082-4
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DOI: https://doi.org/10.1007/s10231-003-0082-4