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    An Optimal Transport Approach for the Kinetic Bohmian Equation

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    Type
    Article
    Authors
    Gangbo, W.
    Haskovec, Jan
    Markowich, Peter A. cc
    Sierra Nunez, Jesus Alfredo cc
    KAUST Department
    Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
    Applied Mathematics and Computational Science Program
    Date
    2019-03-23
    Online Publication Date
    2019-03-23
    Print Publication Date
    2019-04
    Permanent link to this record
    http://hdl.handle.net/10754/652828
    
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    Abstract
    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 Nature
    Journal
    Journal of Mathematical Sciences
    DOI
    10.1007/s10958-019-04248-3
    Additional Links
    http://link.springer.com/article/10.1007/s10958-019-04248-3
    ae974a485f413a2113503eed53cd6c53
    10.1007/s10958-019-04248-3
    Scopus Count
    Collections
    Articles; Applied Mathematics and Computational Science Program; Computer, Electrical and Mathematical Science and Engineering (CEMSE) Division

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