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Regular Lagrangian flow for explicit ODE with discontinuous right-hand side

No. The theory of Regular Lagrangian Flows rests on two key assumptions: a Sobolev/BV regularity of the vector field and a bound from below on its divergence. In your case you are solving $$ X'=b(X) $ …
Nicola Gigli's user avatar
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Reference request: Wasserstein metric spaces for non linear weights/mobility?

Yes, this issue has been considered. You can start having a look at `A new class of transport distances between measures' by Dolbeault, Nazaret and Savaré (http://link.springer.com/article/10.1007%2F …
Nicola Gigli's user avatar