Article
MSC:
35Q35,
74D10,
76D05,
76N15,
76Y05,
81V35,
82D15 | MR 1844272 | Zbl 1050.76063 | DOI: 10.21136/MB.2001.134011
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Keywords:
compressible-Navier-Stokes-Schrödinger; time-dependent-Hartree-Fock approximation; local existence; global existence
compressible-Navier-Stokes-Schrödinger; time-dependent-Hartree-Fock approximation; local existence; global existence
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.
References:
[1] P. Bonche, S. Koonin, J. W. Negele: One-dimensional nuclear dynamics in the TDHF approximation. Phys. Rev. C 13 (1976), 1226–1258. DOI 10.1103/PhysRevC.13.1226
[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. DOI 10.1016/0375-9474(84)90012-5
[3] J. Dechargé, D. Gogny: Hartree-Fock-Bogolyubov calculations with the D1 effective interaction on spherical nuclei. Phys. Rev. C 21 (1980), 1568–1593. DOI 10.1103/PhysRevC.21.1568
[4] B. Ducomet: Global existence for a simplified model of nuclear fluid in one dimension. J. Math. Fluid Mech. 2 (2000), 1–15. DOI 10.1007/s000210050017 | MR 1755864 | Zbl 0974.76013
[5] B. Ducomet, W. M. Zajaczkowski: On simplified models of nuclear fluids. In preparation.
[6] A. L. Fetter, J. D. Walecka: Quantum Theory of Many-Particle Systems. McGraw-Hill, 1971.
[7] K. Kuttler, D. Hicks: Weak solutions of initial-boundary value problems for class of nonlinear viscoelastic equations. Appl. Anal. 26 (1987), 33–43. DOI 10.1080/00036818708839699 | MR 0916897
[8] P. Ring, P. Schuck: The Nuclear Many-Body Problem. Springer Verlag, 1980. MR 0611683
[9] E. Sureau: La matière nucléaire. Hermann, 1998.
[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
[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
[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).
[13] C. Y. Wong, J. A. Maruhn, T. A. Welton: Dynamics of nuclear fluids. I. Foundations. Nucl. Phys. A253 (1975), 469–489.
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