| Title:
|
Simplified models of quantum fluids in nuclear physics (English) |
| Author:
|
Ducomet, B. |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
126 |
| Issue:
|
2 |
| Year:
|
2001 |
| Pages:
|
323-336 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
compressible-Navier-Stokes-Schrödinger |
| Keyword:
|
time-dependent-Hartree-Fock approximation |
| Keyword:
|
local existence |
| Keyword:
|
global existence |
| MSC:
|
35Q35 |
| MSC:
|
74D10 |
| MSC:
|
76D05 |
| MSC:
|
76N15 |
| MSC:
|
76Y05 |
| MSC:
|
81V35 |
| MSC:
|
82D15 |
| idZBL:
|
Zbl 1050.76063 |
| idMR:
|
MR1844272 |
| DOI:
|
10.21136/MB.2001.134011 |
| . |
| Date available:
|
2009-09-24T21:51:06Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134011 |
| . |
| Reference:
|
[1] P. Bonche, S. Koonin, J. W. Negele: One-dimensional nuclear dynamics in the TDHF approximation.Phys. Rev. C 13 (1976), 1226–1258. 10.1103/PhysRevC.13.1226 |
| Reference:
|
[2] N. L. Balazs, B. Schürmann, K. Dietrich, L. P. Csernai: Scaling properties in the hydrodynamical description of heavy-ion reactions.Nucl. Phys. A424 (1984), 605–626. 10.1016/0375-9474(84)90012-5 |
| Reference:
|
[3] J. Dechargé, D. Gogny: Hartree-Fock-Bogolyubov calculations with the D1 effective interaction on spherical nuclei.Phys. Rev. C 21 (1980), 1568–1593. 10.1103/PhysRevC.21.1568 |
| Reference:
|
[4] B. Ducomet: Global existence for a simplified model of nuclear fluid in one dimension.J. Math. Fluid Mech. 2 (2000), 1–15. Zbl 0974.76013, MR 1755864, 10.1007/s000210050017 |
| Reference:
|
[5] B. Ducomet, W. M. Zajaczkowski: On simplified models of nuclear fluids. In preparation.. |
| Reference:
|
[6] A. L. Fetter, J. D. Walecka: Quantum Theory of Many-Particle Systems.McGraw-Hill, 1971. |
| Reference:
|
[7] K. Kuttler, D. Hicks: Weak solutions of initial-boundary value problems for class of nonlinear viscoelastic equations.Appl. Anal. 26 (1987), 33–43. MR 0916897, 10.1080/00036818708839699 |
| Reference:
|
[8] P. Ring, P. Schuck: The Nuclear Many-Body Problem.Springer Verlag, 1980. MR 0611683 |
| Reference:
|
[9] E. Sureau: La matière nucléaire.Hermann, 1998. |
| Reference:
|
[10] G. Ströhmer, W. M. Zajaczkowski: On the existence and properties of the rotationally symmetric equilibrium states of compressible barotropic self-gravitating fluids.Indiana Math. Journal 46 (1997), 1181–1220. MR 1631576 |
| Reference:
|
[11] G. Ströhmer, W. M. Zajaczkowski: Local existence of solutions of free boundary problem for the equations of compressible barotropic viscous self-gravitating fluids.Preprint (1998). MR 1683284 |
| Reference:
|
[12] G. Ströhmer, W. M. Zajaczkowski: On stability of certain equilibrium solution for compressible barotropic viscous self-gravitating fluid motions bounded by a free surface.Preprint (1998). |
| Reference:
|
[13] C. Y. Wong, J. A. Maruhn, T. A. Welton: Dynamics of nuclear fluids. I. Foundations.Nucl. Phys. A253 (1975), 469–489. |
| . |
