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Global Existence of Finite Energy Weak Solutions of Quantum Navier–Stokes Equations

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Abstract

In this paper we consider the Quantum Navier–Stokes system both in two and in three space dimensions and prove the global existence of finite energy weak solutions for large initial data. In particular, the notion of weak solutions is the standard one. This means that the vacuum region is included in the weak formulation. In particular, no extra terms like damping or cold pressure are added to the system in order to define the velocity field in the vacuum region. The main contribution of this paper is the construction of a regular approximating system consistent with the effective velocity transformation needed to get the necessary a priori estimates.

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Authors and Affiliations

  1. GSSI - Gran Sasso Science Institute, Viale Francesco Crispi 7, 67100, L’Aquila, Italy

    Paolo Antonelli

  2. DISIM - Dipartimento di Ingegneria Informatica e Scienze dell’Informazione e Matematica, Via Vetoio, 67100, L’Aquila, Italy

    Stefano Spirito

Authors
  1. Paolo Antonelli
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  2. Stefano Spirito
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Correspondence to Paolo Antonelli.

Additional information

Communicated by G. Friesecke

We would like to thank Prof. Jing Li for some useful comments. The authors would also like to thank one of the two anonimous referees for his very careful reading of our manuscript and for giving us useful comments.

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Antonelli, P., Spirito, S. Global Existence of Finite Energy Weak Solutions of Quantum Navier–Stokes Equations. Arch Rational Mech Anal 225, 1161–1199 (2017). https://doi.org/10.1007/s00205-017-1124-1

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  • DOI: https://doi.org/10.1007/s00205-017-1124-1

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