Simplified models of quantum fluids in nuclear physics

Bernard Ducomet

Mathematica Bohemica (2001)

  • Volume: 126, Issue: 2, page 323-336
  • ISSN: 0862-7959

Abstract

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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.

How to cite

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Ducomet, Bernard. "Simplified models of quantum fluids in nuclear physics." Mathematica Bohemica 126.2 (2001): 323-336. <http://eudml.org/doc/248843>.

@article{Ducomet2001,
abstract = {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.},
author = {Ducomet, Bernard},
journal = {Mathematica Bohemica},
keywords = {compressible-Navier-Stokes-Schrödinger; time-dependent-Hartree-Fock approximation; local existence; global existence},
language = {eng},
number = {2},
pages = {323-336},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Simplified models of quantum fluids in nuclear physics},
url = {http://eudml.org/doc/248843},
volume = {126},
year = {2001},
}

TY - JOUR
AU - Ducomet, Bernard
TI - Simplified models of quantum fluids in nuclear physics
JO - Mathematica Bohemica
PY - 2001
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 126
IS - 2
SP - 323
EP - 336
AB - 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.
LA - eng
KW - compressible-Navier-Stokes-Schrödinger; time-dependent-Hartree-Fock approximation; local existence; global existence
UR - http://eudml.org/doc/248843
ER -

References

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  8. The Nuclear Many-Body Problem, Springer Verlag, 1980. (1980) MR0611683
  9. La matière nucléaire, Hermann, 1998. (1998) 
  10. On the existence and properties of the rotationally symmetric equilibrium states of compressible barotropic self-gravitating fluids, Indiana Math. Journal 46 (1997), 1181–1220. (1997) MR1631576
  11. Local existence of solutions of free boundary problem for the equations of compressible barotropic viscous self-gravitating fluids, Preprint (1998). (1998) MR1683284
  12. On stability of certain equilibrium solution for compressible barotropic viscous self-gravitating fluid motions bounded by a free surface, Preprint (1998). (1998) 
  13. Dynamics of nuclear fluids. I. Foundations, Nucl. Phys. A253 (1975), 469–489. (1975) 

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