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Transport equations with partially B V velocities

Nicolas Lerner (2004)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

We prove the uniqueness of weak solutions for the Cauchy problem for a class of transport equations whose velocities are partially with bounded variation. Our result deals with the initial value problem t u + X u = f , u | t = 0 = g , where X is the vector fieldwith a boundedness condition on the divergence of each vector field a 1 , a 2 . This model was studied in the paper [LL] with a W 1 , 1 regularity assumption replacing our B V hypothesis. This settles partly a question raised in the paper [Am]. We examine the details of the argument of...

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