Schrödinger-Navier-Stokes equation for capillary fluids
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866917449769680896 |
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| author | Salasnich, Luca Succi, Sauro Tiribocchi, Adriano |
| author_facet | Salasnich, Luca Succi, Sauro Tiribocchi, Adriano |
| contents | We highlight some properties of the Schrödinger-Navier-Stokes (SNS) equation [Salasnich, Succi, and Tiribocchi (2024)] of potential relevance for microfluidics and soft matter. Specifically, we show that the SNS equationwith generic parameters is formally equivalent to the Navier-Stokes-Korteweg equations for capillary fluids, with the equivalence established at the level of an action functional that decomposes naturally into a Korteweg conservative and a Rayleigh dissipative components, respectively. We derive the dispersion relation for sound modes, showing that the dispersive parameter controls capillary stiffness while the dissipative parameter controls viscous damping, and that the Bogoliubov dispersion relation is recovered in the quantum limit. We also derive an effective one-dimensional SNS equation for a fluid confined in a narrow capillary tube. Finally, it is argued that the SNS may facilitate the quantum simulation of complex states of flowing matter. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_11747 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Schrödinger-Navier-Stokes equation for capillary fluids Salasnich, Luca Succi, Sauro Tiribocchi, Adriano Fluid Dynamics Quantum Gases Soft Condensed Matter We highlight some properties of the Schrödinger-Navier-Stokes (SNS) equation [Salasnich, Succi, and Tiribocchi (2024)] of potential relevance for microfluidics and soft matter. Specifically, we show that the SNS equationwith generic parameters is formally equivalent to the Navier-Stokes-Korteweg equations for capillary fluids, with the equivalence established at the level of an action functional that decomposes naturally into a Korteweg conservative and a Rayleigh dissipative components, respectively. We derive the dispersion relation for sound modes, showing that the dispersive parameter controls capillary stiffness while the dissipative parameter controls viscous damping, and that the Bogoliubov dispersion relation is recovered in the quantum limit. We also derive an effective one-dimensional SNS equation for a fluid confined in a narrow capillary tube. Finally, it is argued that the SNS may facilitate the quantum simulation of complex states of flowing matter. |
| title | Schrödinger-Navier-Stokes equation for capillary fluids |
| topic | Fluid Dynamics Quantum Gases Soft Condensed Matter |
| url | https://arxiv.org/abs/2604.11747 |