On the low Mach number limit for 2D Navier-Stokes-Korteweg systems

Hientzsch LE (2023)
Mathematics in Engineering 5(2): 1-26.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Abstract / Bemerkung
This paper addresses the low Mach number limit for two-dimensional Navier-Stokes- Korteweg systems. The primary purpose is to investigate the relevance of the capillarity tensor for the analysis. For the sake of a concise exposition, our considerations focus on the case of the quantum Navier-Stokes (QNS) equations. An outline for a subsequent generalization to general viscosity and capillarity tensors is provided. Our main result proves the convergence of finite energy weak solutions of QNS to the unique Leray-Hopf weak solutions of the incompressible Navier-Stokes equations, for general initial data without additional smallness or regularity assumptions. We rely on the compactness properties stemming from energy and BD-entropy estimates. Strong convergence of acoustic waves is proven by means of refined Strichartz estimates that take into account the alteration of the dispersion relation due to the capillarity tensor. For both steps, the presence of a suitable capillarity tensor is pivotal.
Stichworte
Navier-Stokes-Korteweg equation; incompressible Navier-Stokes equation; capillarity; quantum fluids; low Mach number limit; acoustic waves; Strichartz estimates; energy estimates; BD-entropy estimates
Erscheinungsjahr
2023
Zeitschriftentitel
Mathematics in Engineering
Band
5
Ausgabe
2
Seite(n)
1-26
eISSN
2640-3501
Page URI
https://pub.uni-bielefeld.de/record/2963004

Zitieren

Hientzsch LE. On the low Mach number limit for 2D Navier-Stokes-Korteweg systems. Mathematics in Engineering. 2023;5(2):1-26.
Hientzsch, L. E. (2023). On the low Mach number limit for 2D Navier-Stokes-Korteweg systems. Mathematics in Engineering, 5(2), 1-26. https://doi.org/10.3934/mine.2023023
Hientzsch, L. E. (2023). On the low Mach number limit for 2D Navier-Stokes-Korteweg systems. Mathematics in Engineering 5, 1-26.
Hientzsch, L.E., 2023. On the low Mach number limit for 2D Navier-Stokes-Korteweg systems. Mathematics in Engineering, 5(2), p 1-26.
L.E. Hientzsch, “On the low Mach number limit for 2D Navier-Stokes-Korteweg systems”, Mathematics in Engineering, vol. 5, 2023, pp. 1-26.
Hientzsch, L.E.: On the low Mach number limit for 2D Navier-Stokes-Korteweg systems. Mathematics in Engineering. 5, 1-26 (2023).
Hientzsch, Lars Eric. “On the low Mach number limit for 2D Navier-Stokes-Korteweg systems”. Mathematics in Engineering 5.2 (2023): 1-26.
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2022-05-19T09:28:29Z
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