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dc.contributor.authorBardos, Claude W.
dc.contributor.authorGolse, François
dc.contributor.authorMarkowich, Peter A.
dc.contributor.authorPaul, Thierry A.
dc.date.accessioned2015-08-12T09:28:57Z
dc.date.available2015-08-12T09:28:57Z
dc.date.issued2014-12-27
dc.identifier.issn00039527
dc.identifier.doi10.1007/s00205-014-0829-7
dc.identifier.urihttp://hdl.handle.net/10754/566116
dc.description.abstractConsider a monokinetic probability measure on the phase space (Formula presented.) , i.e. (Formula presented.) where Uin is a vector field on RN and ρin a probability density on RN. Let Φt be a Hamiltonian flow on RN × RN. In this paper, we study the structure of the transported measure (Formula presented.) and of its integral in the ξ variable denoted ρ(t). In particular, we give estimates on the number of folds in (Formula presented.) , on which μ(t) is concentrated. We explain how our results can be applied to investigate the classical limit of the Schrödinger equation by using the formalism of Wigner measures. Our formalism includes initial momentum profiles Uin with much lower regularity than required by the WKB method. Finally, we discuss a few examples showing that our results are sharp.
dc.description.sponsorshipPeter Markowich thanks the Fondation des Sciences Mathematiques de Paris for its support during the preparation of this paper.
dc.publisherSpringer Nature
dc.titleHamiltonian Evolution of Monokinetic Measures with Rough Momentum Profile
dc.typeArticle
dc.contributor.departmentApplied Mathematics and Computational Science Program
dc.contributor.departmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
dc.identifier.journalArchive for Rational Mechanics and Analysis
dc.contributor.institutionLaboratoire J.-L. Lions, Université Paris-Diderot, 4 place Jussieu, BP187Paris Cedex 05, France
dc.contributor.institutionEcole Polytechnique, Centre de Mathématiques Laurent Schwartz (CMLS)Palaiseau Cedex, France
dc.contributor.institutionCNRS and Ecole Polytechnique, Centre de Mathématiques Laurent Schwartz (CMLS)Palaiseau Cedex, France
dc.identifier.arxividarXiv:1207.5927v2
kaust.personMarkowich, Peter A.
dc.date.published-online2014-12-27
dc.date.published-print2015-07


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