Geodesic
Simplified models of quantum fluids in nuclear physics
Mathematica Bohemica, Tome 126 (2001) no. 2, pp. 323-336.

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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.
DOI : 10.21136/MB.2001.134011
Classification : 35Q35, 74D10, 76D05, 76N15, 76Y05, 81V35, 82D15
Keywords: compressible-Navier-Stokes-Schrödinger; time-dependent-Hartree-Fock approximation; local existence; global existence 
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Ducomet, B. Simplified models of quantum fluids in nuclear physics. Mathematica Bohemica, Tome 126 (2001) no. 2, pp. 323-336. doi : 10.21136/MB.2001.134011. http://geodesic.mathdoc.fr/articles/10.21136/MB.2001.134011/

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