Type
ArticleKAUST Department
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) DivisionApplied Mathematics and Computational Science Program
Date
2019-03-23Online Publication Date
2019-03-23Print Publication Date
2019-04Permanent link to this record
http://hdl.handle.net/10754/652828
Metadata
Show full item recordAbstract
the existence theory of solutions of the kinetic Bohmian equation, a nonlinear Vlasov-type equation proposed for the phase-space formulation of Bohmian mechanics. Our main idea is to interpret the kinetic Bohmian equation as a Hamiltonian system defined on an appropriate Poisson manifold built on a Wasserstein space. We start by presenting an existence theory for stationary solutions of the kinetic Bohmian equation. Afterwards, we develop an approximative version of our Hamiltonian system in order to study its associated flow. We then prove the existence of solutions of our approximative version. Finally, we present some convergence results for the approximative system; our aim is to show that, in the limit, the approximative solution satisfies the kinetic Bohmian equation in a weak sense.Citation
Gangbo W, Haskovec J, Markowich P, Sierra J (2019) An Optimal Transport Approach for the Kinetic Bohmian Equation. Journal of Mathematical Sciences 238: 415–452. Available: http://dx.doi.org/10.1007/s10958-019-04248-3.Sponsors
The research of W. Gangbo was supported by the NSF grant DMS–1160939.Publisher
Springer NatureJournal
Journal of Mathematical SciencesAdditional Links
http://link.springer.com/article/10.1007/s10958-019-04248-3ae974a485f413a2113503eed53cd6c53
10.1007/s10958-019-04248-3