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

Abstract : We prove quantitative estimates on flows of ordinary differential equations with vector field with gradient given by a singular integral of an $L^1$ 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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Submitted on : Tuesday, August 21, 2012 - 4:33:01 PM
Last modification on : Monday, March 30, 2020 - 12:04:02 PM
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François Bouchut, Gianluca Crippa. Lagrangian flows for vector fields with gradient given by a singular integral. Journal of Hyperbolic Differential Equations, World Scientific Publishing, 2013, 10 (2), pp.235-282. ⟨10.1142/S0219891613500100⟩. ⟨hal-00724586⟩

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