Lagrangian flows for vector fields with gradient given by a singular integral

  title={Lagrangian flows for vector fields with gradient given by a singular integral},
  author={F. Bouchut and Gianluca Crippa},
  journal={Journal of Hyperbolic Differential Equations},
We prove quantitative estimates on flows of ordinary differential equations with vector field with gradient given by a singular integral of an L1 function. Such estimates allow to prove existence, uniqueness, quantitative stability and compactness for the flow, going beyond the BV theory. We illustrate the related well-posedness theory of Lagrangian solutions to the continuity and transport equations. 
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