Hamiltonian Evolution of Monokinetic Measures with Rough Momentum Profile
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| 008 | 210128e20150701xx s 000 0 eng | ||
| 024 | 7 | 0 | |a 10.1007/s00205-014-0829-7 |2 doi |
| 035 | |a (NATIONALLICENCE)springer-10.1007/s00205-014-0829-7 | ||
| 245 | 0 | 0 | |a Hamiltonian Evolution of Monokinetic Measures with Rough Momentum Profile |h [Elektronische Daten] |c [Claude Bardos, François Golse, Peter Markowich, Thierry Paul] |
| 520 | 3 | |a Consider a monokinetic probability measure on the phase space $${{\bf R}^N_{x} \times {\bf R}^N_{\xi}}$$ R x N × R ξ N , i.e. $${\mu^{\rm {in}} = \rho^{\rm {in}}(x)\delta(\xi - U^{\rm {in}}(x))}$$ μ in = ρ in ( x ) δ ( ξ - U in ( x ) ) where U in is a vector field on R N and ρ in a probability density on R N . Let Φ t be a Hamiltonian flow on R N × R N . In this paper, we study the structure of the transported measure $${\mu(t) := \Phi_t\#\mu^{\rm {in}}}$$ μ ( t ) : = Φ t # μ in and of its integral in the ξ variable denoted ρ(t). In particular, we give estimates on the number of folds in $${\Phi_t({\rm graph of} U^{\rm {in}})}$$ Φ t ( graph of U in ) , on whichμ ( 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 U in with much lower regularity than required by the WKB method. Finally, we discuss a few examples showing that our results are sharp. | |
| 540 | |a Springer-Verlag Berlin Heidelberg, 2014 | ||
| 700 | 1 | |a Bardos |D Claude |u Laboratoire J.-L. Lions, Université Paris-Diderot, 4 place Jussieu, BP187, 75252, Paris Cedex 05, France |4 aut | |
| 700 | 1 | |a Golse |D François |u Ecole Polytechnique, Centre de Mathématiques Laurent Schwartz (CMLS), 91128, Palaiseau Cedex, France |4 aut | |
| 700 | 1 | |a Markowich |D Peter |u MCSE Division, King Abdullah University of Science and Technology (KAUST), 23955-6900, Thuwal, Saudi Arabia |4 aut | |
| 700 | 1 | |a Paul |D Thierry |u CNRS and Ecole Polytechnique, Centre de Mathématiques Laurent Schwartz (CMLS), 91128, Palaiseau Cedex, France |4 aut | |
| 773 | 0 | |t Archive for Rational Mechanics and Analysis |d Springer Berlin Heidelberg |g 217/1(2015-07-01), 71-111 |x 0003-9527 |q 217:1<71 |1 2015 |2 217 |o 205 | |
| 856 | 4 | 0 | |u https://doi.org/10.1007/s00205-014-0829-7 |q text/html |z Onlinezugriff via DOI |
| 898 | |a BK010053 |b XK010053 |c XK010000 | ||
| 900 | 7 | |a Metadata rights reserved |b Springer special CC-BY-NC licence |2 nationallicence | |
| 908 | |D 1 |a research-article |2 jats | ||
| 949 | |B NATIONALLICENCE |F NATIONALLICENCE |b NL-springer | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.1007/s00205-014-0829-7 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Bardos |D Claude |u Laboratoire J.-L. Lions, Université Paris-Diderot, 4 place Jussieu, BP187, 75252, Paris Cedex 05, France |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Golse |D François |u Ecole Polytechnique, Centre de Mathématiques Laurent Schwartz (CMLS), 91128, Palaiseau Cedex, France |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Markowich |D Peter |u MCSE Division, King Abdullah University of Science and Technology (KAUST), 23955-6900, Thuwal, Saudi Arabia |4 aut | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Paul |D Thierry |u CNRS and Ecole Polytechnique, Centre de Mathématiques Laurent Schwartz (CMLS), 91128, Palaiseau Cedex, France |4 aut | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Archive for Rational Mechanics and Analysis |d Springer Berlin Heidelberg |g 217/1(2015-07-01), 71-111 |x 0003-9527 |q 217:1<71 |1 2015 |2 217 |o 205 | ||