Lagrangian solutions to the Vlasov-Poissosystem with a point charge

Crippa, Gianluca and Ligabue, Silvia and Saffirio, Chiara. (2018) Lagrangian solutions to the Vlasov-Poissosystem with a point charge. Kinetic and related models, 11 (6). pp. 1277-1299.

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Official URL: http://edoc.unibas.ch/58742/

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We consider the Cauchy problem for the repulsive Vlasov-Poisson system in the three dimensional space, where the initial datum is the sum of a diffuse density, assumed to be bounded and integrable, and a point charge. Under some decay assumptions for the diffuse density close to the point charge, under bounds on the total energy, and assuming that the initial total diffuse charge is strictly less than one, we prove existence of global Lagrangian solutions. Our result extends the Eulerian theory of [17], proving that solutions are transported by the flow trajectories. The proof is based on the ODE theory developed in [8] in the setting of vector fields with anisotropic regularity, where some components of the gradient of the vector field is a singular integral of a measure.
Faculties and Departments:05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Analysis (Crippa)
UniBasel Contributors:Crippa, Gianluca and Ligabue, Silvia
Item Type:Article, refereed
Article Subtype:Research Article
Note:Publication type according to Uni Basel Research Database: Journal article
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edoc DOI:
Last Modified:15 Jan 2019 13:41
Deposited On:24 Aug 2018 13:46

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