Semiclassical limit and well-posedness of nonlinear Schrödinger-Poisson systems.
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Li, Hailiang, Lin, Chi-Kun (2003)
Electronic Journal of Differential Equations (EJDE) [electronic only]
Fanghua Lin, Ping Zhang (2004/2005)
Séminaire Équations aux dérivées partielles
In this paper, we study the semiclassical limit of the cubic nonlinear Schrödinger equation with the Neumann boundary condition in an exterior domain. We prove that before the formation of singularities in the limit system, the quantum density and the quantum momentum converge to the unique solution of the compressible Euler equation with the slip boundary condition as the scaling parameter approaches
Joel Smoller, Blake Temple (1994)
Journées équations aux dérivées partielles
Elias M. Smoller, Blake Temple (1995)
Journées équations aux dérivées partielles
Bernard Ducomet (2001)
Mathematica Bohemica
We revisit a hydrodynamical model, derived by Wong from Time-Dependent-Hartree-Fock approximation, to obtain a simplified version of nuclear matter. We obtain well-posed problems of Navier-Stokes-Poisson-Yukawa type, with some unusual features due to quantum aspects, for which one can prove local existence. In the case of a one-dimensional nuclear slab, we can prove a result of global existence, by using a formal analogy with some model of nonlinear "viscoelastic" rods.
К. Малышев (1995)
Zapiski naucnych seminarov POMI
Alberto Strumia (1983)
Annales de l'I.H.P. Physique théorique
A. M. Blokhin, V. Romano, Yu. L. Trakhinin (1997)
Annales de l'I.H.P. Physique théorique
Paul, S.N., Chakraborty, B., Debnath, L. (1985)
International Journal of Mathematics and Mathematical Sciences
Giuseppe Arcidiacono (1976)
Collectanea Mathematica
Gérard A. Maugin (1974)
Annales de l'I.H.P. Physique théorique
B. Linet (1971)
Annales de l'I.H.P. Physique théorique
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