Simplified models of quantum fluids in nuclear physics. (English) Zbl 1050.76063

Ducomet, B.

Math. Bohem. 126, No. 2, 323-336 (2001).

Summary: We revisit a hydrodynamical model derived 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 global existence, by using a formal analogy with some model of nonlinear “viscoelastic” rods.

MSC:

76Y05	Quantum hydrodynamics and relativistic hydrodynamics
82D15	Statistical mechanics of liquids
35Q35	PDEs in connection with fluid mechanics

Keywords:

time-dependent-Hartree-Fock approximation; local existence; global existence