Open AccessRemarks on the derivation of finite energy weak solutions to the QHD system
Author(s) -
Paolo Antonelli
Publication year - 2021
Publication title -
proceedings of the american mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.968
H-Index - 84
eISSN - 1088-6826
pISSN - 0002-9939
DOI - 10.1090/proc/14502
Subject(s) - a priori and a posteriori , regularization (linguistics) , novelty , class (philosophy) , quantum , mathematics , computer science , physics , quantum mechanics , philosophy , theology , epistemology , artificial intelligence
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.