Remarks on the derivation of finite energy weak solutions to the QHD system

Antonelli, Paolo

doi:10.1090/proc/14502

Remarks on the derivation of finite energy weak solutions to the QHD system
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by Paolo Antonelli

Proc. Amer. Math. Soc. 149 (2021), 1985-1997

DOI: https://doi.org/10.1090/proc/14502

Published electronically: February 24, 2021

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Abstract:

In this note we give an alternative proof of existence of finite energy weak solutions to the quantum hydrodynamics (QHD) system. The main novelty in our approach is that no regularization procedure or approximation is needed, as it is only based on the integral formulation of NLS equation and the a priori bounds given by the Strichartz estimates. The main advantage of this proof is that it can be applied to a wider class of QHD systems.

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