Low Mach number limit for the quantum hydrodynamics system

Donatelli, Donatella; Marcati, Pierangelo

doi:10.1186/s40687-016-0063-z

Cited by 25 publications

(12 citation statements)

References 28 publications

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“…The ε-limit should be interpreted as scaling limit for the healing length ε going to 0 and does not coincide with the semi-classical limit. The ε-limit for (5) posed on T d for d = 2, 3 has been studied in [14]. Due to absence of significant dispersion on periodic domains, more regular solutions to (5) and convergence to local strong solutions is considered.…”

Section: Theorem 41 ([1]mentioning

confidence: 99%

Analysis of acoustic oscillations for a class of hydrodynamic systems describing quantum fluids

Antonelli¹,

Hientzsch²,

Marcati³

2020

Preprint

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Hydrodynamic systems for quantum fluids are systems for compressible fluid flows for which quantum effects are macroscopically relevant. We discuss how the presence of the dispersive tensor describing the quantum effects alters the acoustic dispersion at the example of the Quantum Hydrodynamic system (QHD). For the QHD system the dispersion relation is given by the Bogoliubov dispersion relation for weakly interacting Bose gases. We provide refined Strichartz estimates allowing for an accurate control of acoustic oscillations. Applications to the low Mach number limit for the quantum Navier-Stokes equations and the QHD system are discussed. The dispersive analysis generalizes to some Euler-and Navier-Stokes-Korteweg systems for capillary fluids.

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Section: Theorem 41 ([1]mentioning

confidence: 99%

Analysis of acoustic oscillations for a class of hydrodynamic systems describing quantum fluids

Antonelli¹,

Hientzsch²,

Marcati³

2020

Preprint

Self Cite

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“…We finally investigate the relative entropy with respect to equilibrium that is a natural distance to equilibrium. Relative entropies have been found to be key tools for investigating hyperbolic as well as hyperbolic-parabolic systems [5,7,22,6,41,36,11,26,9,1,20,4]. The relative entropy with respect to equilibrium is nonnegative by the convexity of η and locally behaves quadratically with respect to q.…”

Section: (U 3 )mentioning

confidence: 99%

Relaxation Limit and Initial-Layers for a Class of Hyperbolic-Parabolic Systems

Giovangigli¹,

Yang²,

Yong³

2018

SIAM J. Math. Anal.

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We consider a class of hyperbolic-parabolic systems with small diffusion terms and stiff sources. Existence of solutions to the Cauchy problem with ill prepared initial data is established by using composite expansions including initial-layer correctors and a convergence-stability lemma. New multitime expansions are introduced and lead to second-order error estimates between the composite expansions and the solution. Reduced equilibrium systems of second-order accuracy are also investigated as well as initial-layers of Chapman-Enskog expansions.

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“…Non-uniqueness results by using convex integration methods have been proved in [18]. Relative entropy methods to study singular limits for equations (1.4)-(1.6) have been exploited in [12,15,18,20,24]; in particular we mention the incompressible limit in [1] in the quantum case, the quasineutral limit in [19] for the constant capillarity case and the vanishing viscosity limit in [12]. The analysis of the long time behaviour for the isothermal quantum Navier-Stokes equations has been performed in [16].…”

Section: Introductionmentioning

confidence: 99%

Global existence of weak solutions to the Navier–Stokes–Korteweg equations

Antonelli

Spirito²

2022

Ann. Inst. H. Poincaré Anal. Non Linéaire

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In this paper we consider the Navier-Stokes-Korteweg equations for a viscous compressible fluid with capillarity effects in three space dimensions. We prove global existence of finite energy weak solutions for large initial data. Contrary to previous results regarding this system, vacuum regions are considered in the definition of weak solutions and no additional damping terms are considered. The convergence of the approximating solutions is obtained by introducing suitable truncations of the velocity field and the mass density at different scales in the momentum equations and use only the a priori bounds obtained by the energy and the Bresch-Desjardins entropy. Moreover, the approximating solutions enjoy only a limited amount of regularity, and the derivation of the truncations of the velocity and the density is performed by a suitable regularization procedure.

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Low Mach number limit for the quantum hydrodynamics system

Cited by 25 publications

References 28 publications

Analysis of acoustic oscillations for a class of hydrodynamic systems describing quantum fluids

Analysis of acoustic oscillations for a class of hydrodynamic systems describing quantum fluids

Relaxation Limit and Initial-Layers for a Class of Hyperbolic-Parabolic Systems

Global existence of weak solutions to the Navier–Stokes–Korteweg equations

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