On the Finite Energy Weak Solutions to a System in Quantum Fluid Dynamics
By Paolo Antonelli, Pierangelo Marcati. 2008
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In this paper we consider the global existence of weak solutions to a class of Quantum Hydrodynamics (QHD) systems with initial data, arbitrarily large in the energy norm. These type of models, initially proposed by Madelung [44], have been extensively used in Physics to investigate Superfluidity and Superconductivity phenomena [19,38] and more recently in the modeling of semiconductor devices [20] . Our approach is based on various tools, namely the wave functions polar decomposition, the construction of approximate solution via a fractional steps method which iterates a Schrödinger Madelung picture with a suitable wave function updating mechanism. Therefore several a priori bounds of energy, dispersive and local smoothing type, allow us to prove the compactness of the approximating sequences. No uniqueness result is provided.
Subfields: Applied Mathematics, Computational Mechanics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/d5c6ca116cfb2d1c1658fbf53d08d2d7a301ff5c
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In Applied Mathematics
In Computational Mechanics
In Mathematical Physics
Citations in the corpus
- Existence of global strong solution and vanishing capillarity-viscosity limit in one dimension for the Korteweg system (2011, background): “Indeed we are in the context of the well known Lax result as the system is also genuinely nonlinear (we refer to”