2019/10/17 by Paolo Antonelli, Pierangelo Marcati, Antonelli, Paolo +3 · 1 citation
Mathematics · Physics and Astronomy · #35Q35 #35Q40 (Primary) #76Y05 #82D50 (Secondary) #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Navier-Stokes equation solutions #Nonlinear Waves and Solitons #Quantum Gases (cond-mat.quant-gas) #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.1910.08104
openalex publication_date 2019/10/17 · openalex created_date 2019/10/25 · openalex updated_date 2026/07/28
In this paper we consider the one dimensional quantum hydrodynamics (QHD) system, with a genuine hydrodynamic approach. The global existence of weak solutions with large data has been obtained in [2, 3], in several space dimensions, by using the connection between the hydrodynamic variables and the Schrödinger wave function. One of the main purposes of the present paper is to overcome the need to postulate the a priori existence of a wave function that generates the hydrodynamic data. Moreover, we introduce a novel functional, related to the chemical potential in the quantum probability density ρ dx, which allow us to obtain stability properties for a large class of weak solutions in the finite energy space.