Coupling Navier-Stokes and Gross-Pitaevskii equations for the numerical simulation of two-fluid quantum flows

Brachet, Marc; Sadaka, Georges; Zhentong, Zhang,; Kalt, Victor; Danaila, Ionut

doi:10.1016/j.jcp.2023.112193

Cited by 3 publications

(1 citation statement)

References 37 publications

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“…Thus, by utilizing appropriate self-interactions (for instance, non-local potentials, or including the normal fluid density), it would be important to test the model against experimental findings. A mathematical guarantee of the existence of solutions to the Pitaevskii model is essential to complement the efforts to numerically simulate such complicated systems [BSZ+23]. It is worth mentioning that a better understanding of superfluidity could be revolutionary to most modern experiments in physics (including the Large Hadron Collider [Leb94,RM18]), and also to the fields of quantum computing [HDT21], gravitational wave astronomy [SDLPS17], and dark matter [vKEE+23].…”

Section: Significance Of the Resultsmentioning

confidence: 99%

Small-data global existence of solutions for the Pitaevskii model of superfluidity

Jang,

Chaitanya Jayanti,

Kukavica

2024

Nonlinearity

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We investigate a micro-scale model of superfluidity derived by Pitaevskii (1959 Sov. Phys. JETP 8 282–7) to describe the interacting dynamics between the superfluid and normal fluid phases of Helium-4. The model involves the nonlinear Schrödinger equation (NLS) and the Navier–Stokes equations, coupled to each other via a bidirectional nonlinear relaxation mechanism. Depending on the nature of the nonlinearity in the NLS, we prove global/almost global existence of solutions to this system in T 2 —strong in wavefunction and velocity, and weak in density.

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Section: Significance Of the Resultsmentioning

confidence: 99%

Small-data global existence of solutions for the Pitaevskii model of superfluidity

Jang,

Chaitanya Jayanti,

Kukavica

2024

Nonlinearity

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On the Mass Transfer in the 3D Pitaevskii Model

Jang,

Jayanti,

Kukavica

2024

J. Math. Fluid Mech.

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We examine a micro-scale model of superfluidity derived by Pitaevskii (Sov. Phys. JETP 8:282-287, 1959) which describes the interacting dynamics between superfluid He-4 and its normal fluid phase. This system consists of the nonlinear Schrödinger equation and the incompressible, inhomogeneous Navier-Stokes equations, coupled to each other via a bidirectional nonlinear relaxation mechanism. The coupling permits mass/momentum/energy transfer between the phases, and accounts for the conversion of superfluid into normal fluid. We prove the existence of global weak solutions in $${\mathbb {T}}^3$$ T 3 for a power-type nonlinearity, beginning from small initial data. The main challenge is to control the inter-phase mass transfer in order to ensure the strict positivity of the normal fluid density, while obtaining time-independent a priori estimates.

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Kelvin Waves, Mutual Friction, and Fluctuations in the Gross–Pitaevskii Model

Krstulovic

Brachet

2023

J Low Temp Phys

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Coupling Navier-Stokes and Gross-Pitaevskii equations for the numerical simulation of two-fluid quantum flows

Cited by 3 publications

References 37 publications

Small-data global existence of solutions for the Pitaevskii model of superfluidity

Small-data global existence of solutions for the Pitaevskii model of superfluidity

On the Mass Transfer in the 3D Pitaevskii Model

Kelvin Waves, Mutual Friction, and Fluctuations in the Gross–Pitaevskii Model

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