Global, finite energy, weak solutions to a magnetic quantum fluid system

Raffaele Scandone; Raffaele Scandone

doi:10.3934/nhm.2025016

Networks and Heterogeneous Media

2025, Volume 20, Issue 2: 345-355. doi: 10.3934/nhm.2025016

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Global, finite energy, weak solutions to a magnetic quantum fluid system

Raffaele Scandone ^,

Dipartimento di Matematica e Applicazioni "R. Caccioppoli", Università degli Studi di Napoli "Federico Ⅱ", Complesso Universitario Monte S. Angelo, via Cintia, 80126, Napoli, Italy

Received: 18 January 2025 Revised: 08 April 2025 Accepted: 14 April 2025 Published: 23 April 2025

In this study, we showed the existence of global, finite energy, weak solutions to a class of compressible Euler equations, describing the dynamics of a quantum fluid interacting with an external magnetic field. To do so, we exploited suitable a priori estimates for weak solutions of the underlying wave-function dynamics, governed by a magnetic semilinear Schrödinger equation.
- quantum hydrodynamics,
- magnetic potentials,
- weak solutions,
- Madelung transform,
- Schrödinger equation
Citation: Raffaele Scandone. Global, finite energy, weak solutions to a magnetic quantum fluid system[J]. Networks and Heterogeneous Media, 2025, 20(2): 345-355. doi: 10.3934/nhm.2025016

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Abstract

In this study, we showed the existence of global, finite energy, weak solutions to a class of compressible Euler equations, describing the dynamics of a quantum fluid interacting with an external magnetic field. To do so, we exploited suitable a priori estimates for weak solutions of the underlying wave-function dynamics, governed by a magnetic semilinear Schrödinger equation.

References

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