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Stability of the global weak axisymmetric solution to the quantum Euler system with vorticity in dimension d = 2

Haspot, Boris; Vassenet, Marc-Antoine (2022), Stability of the global weak axisymmetric solution to the quantum Euler system with vorticity in dimension d = 2. https://basepub.dauphine.psl.eu/handle/123456789/24077

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Type
Document de travail / Working paper
Date
2022
Series title
Cahier de recherche CEREMADE, Université Paris Dauphine-PSL
Published in
Paris
Pages
36
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Author(s)
Haspot, Boris
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Vassenet, Marc-Antoine
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
We consider the stability of the global weak solution of the Quantum Euler system in two space dimensions. More precisely, we establish the compactness of global finite energy weak solution for large initial data provided that the initial data are axisymmetric. The main novelty is that the initial velocity is not necessary irrotational, our main argument is based on a generalization of the Madelung transform which enables to prove new Kato estimates on the irrotational part of the velocity. Contents