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Journal articles
Lagrangian flows for vector fields with anisotropic regularity
Abstract : We prove quantitative estimates for flows of vector fields subject to anisotropic regu-larity conditions: some derivatives of some components are (singular integrals of) measures, while the remaining derivatives are (singular integrals of) integrable functions. This is motivated by the regularity of the vector field in the Vlasov-Poisson equation with measure density. The proof ex-ploits an anisotropic variant of the argument in [19, 13] and suitable estimates for the difference quotients in such anisotropic context. In contrast to regularization methods, this approach gives quantitative estimates in terms of the given regularity bounds. From such estimates it is possible to recover the well posedness for the ordinary differential equation and for Lagrangian solutions to the continuity and transport equations.
Cited literature [27 references]
https://hal-upec-upem.archives-ouvertes.fr/hal-01097370
Contributor : François Bouchut <>
Submitted on : Friday, December 19, 2014 - 3:23:00 PM
Last modification on : Monday, March 30, 2020 - 12:04:02 PM
Long-term archiving on: : Monday, March 23, 2015 - 6:26:11 PM
Contributor : François Bouchut <>
Submitted on : Friday, December 19, 2014 - 3:23:00 PM
Last modification on : Monday, March 30, 2020 - 12:04:02 PM
Long-term archiving on: : Monday, March 23, 2015 - 6:26:11 PM
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anisotropic.pdf
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