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- W2000863553 abstract "The existence of classical solutions to the stationary quantum Navier–Stokes equations in one space dimension is studied. The main idea of the proof is to reformulate the quantum Navier–Stokes equations as the viscous quantum Euler system. The existence of classical solutions to the stationary viscous quantum Euler system is shown by using an exponential variable transformation and the Leray–Schauder fixed-point theorem. As a consequence, the existence of classical solutions to the stationary quantum Navier–Stokes equations can be deduced. On considère le problème de lʼexistence des solutions classiques des équations de Navier–Stokes quantiques stationnaires. Lʼidée essentielle de la démonstration repose sur une reformulation des équations de Navier–Stokes quantiques comme système dʼEuler visqueux quantique. Lʼexistence des solutions classiques statinnaires du système dʼEuler visqueux quantique est établie en utilisant une transformation exponentielle variable et en appliquant le théorème du point fixe de Leray–Schauder. On en déduit alors les solutions classiques des équations de Navier–Stokes quantiques stationnaires." @default.
- W2000863553 created "2016-06-24" @default.
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- W2000863553 date "2011-11-01" @default.
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- W2000863553 title "Classical solutions to one-dimensional stationary quantum Navier–Stokes equations" @default.
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- W2000863553 doi "https://doi.org/10.1016/j.matpur.2011.07.005" @default.
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