Crippa, Gianluca and Ligabue, Silvia and Saffirio, Chiara. (2018) Lagrangian solutions to the VlasovPoissosystem with a point charge. Kinetic and related models, 11 (6). pp. 12771299.
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Official URL: http://edoc.unibas.ch/58742/
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Abstract
We consider the Cauchy problem for the repulsive VlasovPoisson 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 
ISSN:  19375093 
eISSN:  19375077 
Note:  Publication type according to Uni Basel Research Database: Journal article 
Language:  English 
Identification Number: 

edoc DOI:  
Last Modified:  15 Jan 2019 13:41 
Deposited On:  24 Aug 2018 13:46 
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