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

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.


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