Non-unicité du transport par un champ de vecteurs presque BV

Keywords

Geography, Humanities, Philosophy

References

• Flow of Non-Lipschitz Vector-Fields and Navier-Stokes EquationsJ.-Y. Chemin, Nicolás Lerner — 1995
• Transport equation and Cauchy problem for BV vector fieldsLuigi Ambrosio — 2004
• On vector fields as generators of flows: A counterexample to Nelson's conjectureMichael Aizenman — 1978
• Ordinary differential equations, transport theory and Sobolev spacesRonald J. DiPerna, Pierre Louis Lions — 1989
• Uniqueness of continuous solutions for BV vector fieldsFerruccio Colombini, Nicolás Lerner — 2002

Cited by

• A Note on Two-Dimensional Transport with Bounded DivergenceFerruccio Colombini, Gianluca Crippa, Jeffrey Rauch — 2006
• Oscillatory solutions to transport equationsCamillo De Lellis, Gianluca Crippa — 2006
• Uniqueness in the Cauchy problem for transport in R2 and R1+2Ferruccio Colombini, Jeffrey Rauch — 2005
• C^1 measure respecting maps preserve BV if they have bounded derivativeFerruccio Colombini, Tao Luo, Jeffrey Rauch — 2011
• On Bressan's conjecture on mixing properties of vector fieldsStefano Bianchini — 2006
• Uniqueness, Renormalization, and Smooth Approximations for Linear Transport EquationsFrançois Bouchut, Gianluca Crippa — 2006
• Generalized N-property and Sard theorem for Sobolev mapsGiovanni Alberti — 2012
• ODEs with Sobolev coefficients: The eulerian and the lagrangian approachCamillo De Lellis — 2008
• A uniqueness result for the continuity equation in two dimensionsGiovanni Alberti, Stefano Bianchini, Gianluca Crippa — 2014
• Équations de transport à coefficient dont le gradient est donné par une intégrale singulièreFrançois Bouchut, Gianluca Crippa — 2008
• A quantitative theory for the continuity equationChristian Seis — 2016
• Optimal stability estimates for continuity equationsChristian Seis — 2016
• Flows generated by divergence free vector fields with compact supportOlivier Kneuss, Wladimir Neves — 2016
• A uniqueness result for the decomposition of vector fields in Rd[12pt]minimal amsmath wasysym amsfonts amssymb amsbsy mathrsfs upgreek -69pt document$$Stefano Bianchini, Paolo Bonicatto — 2017
• Untangling of trajectories for non-smooth vector fields and Bressan's Compactness ConjecturePaolo Bonicatto — 2017
• Well-posedness of the deterministic transport equation with singular velocity field perturbed along fractional Brownian pathsOussama Amine, Abdol-Reza Mansouri, Frank Proske — 2020
• On solutions of the transport equation in the presence of singularitiesEvelyne Miot, Nicholas Sharples — 2020
• Smoothing does not give a selection principle for transport equations with bounded autonomous fieldsCamillo De Lellis, Vikram Giri — 2020
• Quantitative Estimates for Regular Lagrangian Flows with BV Vector FieldsQuoc‐Hung Nguyen — 2018
• Local Nonuniqueness for Stochastic Transport Equations with Deterministic DriftStefano Modena, Andre Schenke — 2023

Related papers

• Ordinary differential equations, transport theory and Sobolev spacesRonald J. DiPerna, Pierre Louis Lions — 1989
• Transport equation and Cauchy problem for BV vector fieldsLuigi Ambrosio — 2004
• Uniqueness and Nonuniqueness for Nonsmooth Divergence Free TransportFerruccio Colombini, Tao Luo, J. Rauch — 2003
• On vector fields as generators of flows: A counterexample to Nelson's conjectureMichael Aizenman — 1978
• Estimates and regularity results for the DiPerna-Lions flowGianluca Crippa, Camillo De Lellis — 2008
• A lemma and a conjecture on the cost of rearrangementsAlberto Bressan — 2003