Quantum hydrodynamics with nonlinear interactions

DOI10.3934/dcdss.2016.9.1zbMath1332.35307OpenAlexW2525552963WikidataQ58619706 ScholiaQ58619706MaRDI QIDQ258689

Pierangelo Marcati, Paolo Antonelli

Publication date: 10 March 2016

Published in: Discrete and Continuous Dynamical Systems. Series S (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcdss.2016.9.1

zbMATH Keywords

global existencequantum hydrodynamicsnonlocal interactionsBose Einsteinfinite energy

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) NLS equations (nonlinear Schrödinger equations) (35Q55) PDEs in connection with quantum mechanics (35Q40) Statistical mechanics of semiconductors (82D37) Quantum dynamics and nonequilibrium statistical mechanics (general) (82C10)

Related Items (11)

Numerical investigations of dispersive shocks and spectral analysis for linearized quantum hydrodynamics ⋮ Blow-up of the smooth solution to the IBVP of three-dimensional quantum hydrodynamic models ⋮ Existence of standing and traveling waves in quantum hydrodynamics with viscosity ⋮ An intrinsically hydrodynamic approach to multidimensional QHD systems ⋮ Traveling waves for quantum hydrodynamics with nonlinear viscosity ⋮ Dispersive shocks in quantum hydrodynamics with viscosity ⋮ Genuine hydrodynamic analysis to the 1-D QHD system: existence, dispersion and stability ⋮ Remarks on blow-up of the smooth solution to quantum hydrodynamic models in \(\mathbb {R}^{d}\) ⋮ Stability for the quadratic derivative nonlinear Schrödinger equation and applications to the Korteweg-Kirchhoff type Euler equations for quantum hydrodynamics ⋮ Remarks on the derivation of finite energy weak solutions to the QHD system ⋮ Spectral analysis of dispersive shocks for quantum hydrodynamics with nonlinear viscosity

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