Rough continuity and transport equations are well-posed for Osgood and DiPerna-Lions drifts, yielding a rough Yudovich theorem for 2D Euler and a continuous random dynamical system.
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On the well-posedness of (nonlinear) rough continuity equations
Rough continuity and transport equations are well-posed for Osgood and DiPerna-Lions drifts, yielding a rough Yudovich theorem for 2D Euler and a continuous random dynamical system.