Lagrangian flows for vector fields with gradient given by a singular integral
By F. Bouchut, Gianluca Crippa. 2012
79 citations recorded by the source corpus.
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.
Subfields: Applied Mathematics, Control and Systems Engineering, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/f78412a6ce1580c17390f7708871428b4ec577a8
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In Applied Mathematics
- Cristiana De Filippis
- Giuseppe Mingione
- Pierre-Emmanuel Jabin
- Zhenfu Wang
- Giovanni S. Alberti
- Didier Bresch
- A. Mazzucato
- Gianluca Crippa
In Control and Systems Engineering
- Gianluca Crippa
- Didier Bresch
- Pierre-Emmanuel Jabin
- Cristiana De Filippis
- Giuseppe Mingione
- Giovanni S. Alberti
- Zhenfu Wang
- A. Mazzucato
In Mathematical Physics
- Giuseppe Mingione
- Cristiana De Filippis
- Pierre-Emmanuel Jabin
- Gianluca Crippa
- Giovanni S. Alberti
- A. Mazzucato
- Zhenfu Wang
- Didier Bresch
Citations in the corpus
- Lipschitz Bounds and Nonautonomous Integrals (2020, methodology): “We also mention that, over the last years, Sobolev coefficients have ben systematically considered as a replacement of usual Lipschitz ones to find optimal conditions in several other fields of analysis and PDE; see for instance [7, 25].”
- Global existence of weak solutions for compressible Navier--Stokes equations: Thermodynamically unstable pressure and anisotropic viscous stress tensor (2015, background): “This can only be improved with specific additional structure, such as provided by low dimension, see [3, 11, 23, 24, 41], Hamiltonian properties [19, 44], or as a singular integral [10].”
- Exponential self-similar mixing and loss of regularity for continuity equations (2014, background): “The extension to the borderline case p = 1 is still open (see, however, [4]).”
- Mean Field Limit and Propagation of Chaos for Vlasov Systems with Bounded Forces (2015, background): “[ That may sometimes be improved for second order systems like (1.1), see 8], [9], [12], [32].”