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Journal Articles Journal de Mathématiques Pures et Appliquées Year : 2018

Global weak solutions to the compressible quantum navier-stokes equation and its semi-classical limit

Abstract

This paper is dedicated to the construction of global weak solutions to the quantum Navier-Stokes equation, for any initial value with bounded energy and entropy. The construction is uniform with respect to the Planck constant. This allows to perform the semi-classical limit to the associated compressible Navier-Stokes equation. One of the difficulty of the problem is to deal with the degenerate viscosity, together with the lack of integrability on the velocity. Our method is based on the construction of weak solutions that are renormalized in the velocity variable. The existence, and stability of these solutions do not need the Mellet-Vasseur inequality.
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Dates and versions

hal-01347943 , version 1 (22-07-2016)
hal-01347943 , version 2 (26-04-2019)

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Ingrid Lacroix-Violet, Alexis Vasseur. Global weak solutions to the compressible quantum navier-stokes equation and its semi-classical limit. Journal de Mathématiques Pures et Appliquées, 2018, 114, pp.191-210. ⟨10.1016/j.matpur.2017.12.002⟩. ⟨hal-01347943v2⟩
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