MATHEMATICA BOHEMICA, Vol. 126, No. 2, pp. 323-336 (2001)

Simplified models of quantum fluids
in nuclear physics

B. Ducomet

B. Ducomet, CEA-Département de Physique Théorique et Appliquée, BP 12, 91680 Bruyeres-le-Chatel, France, e-mail: ducomet@bruyeres.cea fr

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.

Keywords: compressible-Navier-Stokes-Schrödinger

Classification (MSC2000): 74D10, 76D05, 76N15

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