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compressible-Navier-Stokes-Schrödinger; time-dependent-Hartree-Fock approximation; local existence; global existence
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.
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