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2018 | OriginalPaper | Buchkapitel

7. The Navier-Stokes Equations in a Curved Domain

verfasst von : Gung-Min Gie, Makram Hamouda, Chang-Yeol Jung, Roger M. Temam

Erschienen in: Singular Perturbations and Boundary Layers

Verlag: Springer International Publishing

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Abstract

In fluid dynamics, we often study the flow of liquids and gases inside a region enclosed by a rigid boundary or around such a region. Some interesting applications in this field include analyzing, e.g., the motion of air around airplanes or automobiles to increase the efficiency of motion, the flow of atmosphere and oceans to predict the weather, and the blood flow inside vessels in medicine where the fluid is blood. In all these applications the fluid, such as air, water, or blood, is considered incompressible and its viscosity is usually very small.

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Zurück zum Zitat R. Temam. Infinite-dimensional dynamical systems in mechanics and physics. Applied Mathematical Sciences, 68. Springer-Verlag, New York, 1988. xvi+500 pp.CrossRef R. Temam. Infinite-dimensional dynamical systems in mechanics and physics. Applied Mathematical Sciences, 68. Springer-Verlag, New York, 1988. xvi+500 pp.CrossRef
[Tem01]
Zurück zum Zitat R. Temam. Navier-Stokes equations. AMS Chelsea Publishing, Providence, RI, 2001. Theory and numerical analysis, Reprint of the 1984 edition. R. Temam. Navier-Stokes equations. AMS Chelsea Publishing, Providence, RI, 2001. Theory and numerical analysis, Reprint of the 1984 edition.
[Tem06]
[TW96]
Zurück zum Zitat Roger Temam and Xiaoming Wang. Asymptotic analysis of Oseen type equations in a channel at small viscosity. Indiana Univ. Math. J., 45(3):863–916, 1996.MathSciNetCrossRef Roger Temam and Xiaoming Wang. Asymptotic analysis of Oseen type equations in a channel at small viscosity. Indiana Univ. Math. J., 45(3):863–916, 1996.MathSciNetCrossRef
[TW97b]
Zurück zum Zitat Roger Temam and Xiaoming Wang. On the behavior of the solutions of the Navier-Stokes equations at vanishing viscosity. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 25(3–4):807–828 (1998), 1997. Dedicated to Ennio De Giorgi. Roger Temam and Xiaoming Wang. On the behavior of the solutions of the Navier-Stokes equations at vanishing viscosity. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 25(3–4):807–828 (1998), 1997. Dedicated to Ennio De Giorgi.
[TW98]
Zurück zum Zitat Roger Temam and Xiaoming Wang. Boundary layers for Oseen’s type equation in space dimension three. Russian J. Math. Phys., 5(2):227–246 (1998), 1997.MathSciNetMATH Roger Temam and Xiaoming Wang. Boundary layers for Oseen’s type equation in space dimension three. Russian J. Math. Phys., 5(2):227–246 (1998), 1997.MathSciNetMATH
[TW00]
Zurück zum Zitat R. Temam and X. Wang. Remarks on the Prandtl equation for a permeable wall. ZAMM Z. Angew. Math. Mech., 80(11–12):835–843, 2000. Special issue on the occasion of the 125th anniversary of the birth of Ludwig Prandtl.MathSciNetCrossRef R. Temam and X. Wang. Remarks on the Prandtl equation for a permeable wall. ZAMM Z. Angew. Math. Mech., 80(11–12):835–843, 2000. Special issue on the occasion of the 125th anniversary of the birth of Ludwig Prandtl.MathSciNetCrossRef
[TW02]
Zurück zum Zitat Roger Temam and Xiaoming Wang. Boundary layers associated with incompressible Navier-Stokes equations: the noncharacteristic boundary case. J. Differential Equations, 179 (2002), no. 2, 647–686.MathSciNetCrossRef Roger Temam and Xiaoming Wang. Boundary layers associated with incompressible Navier-Stokes equations: the noncharacteristic boundary case. J. Differential Equations, 179 (2002), no. 2, 647–686.MathSciNetCrossRef
[WXZ12]
Zurück zum Zitat Lizhen Wang, Zhouping Xin, and Aibin Zang. Vanishing viscous limits for 3D Navier-Stokes equations with a Navier-slip boundary condition. Journal of Mathematical Fluid Mechanics, pages 1–35. 10.1007/s00021-012-0103-4. Lizhen Wang, Zhouping Xin, and Aibin Zang. Vanishing viscous limits for 3D Navier-Stokes equations with a Navier-slip boundary condition. Journal of Mathematical Fluid Mechanics, pages 1–35. 10.1007/s00021-012-0103-4.
[Wan01]
Zurück zum Zitat Xiaoming Wang. A Kato type theorem on zero viscosity limit of Navier-Stokes flows. Indiana Univ. Math. J., 50 (Special Issue): 223–241, 2001. Dedicated to Professors Ciprian Foias and Roger Temam (Bloomington, IN, 2000). Xiaoming Wang. A Kato type theorem on zero viscosity limit of Navier-Stokes flows. Indiana Univ. Math. J., 50 (Special Issue): 223–241, 2001. Dedicated to Professors Ciprian Foias and Roger Temam (Bloomington, IN, 2000).
[XX07]
Zurück zum Zitat Yuelong Xiao and Zhouping Xin. On the vanishing viscosity limit for the 3D Navier-Stokes equations with a slip boundary condition. Comm. Pure Appl. Math., 60(7):1027–1055, 2007.MathSciNetCrossRef Yuelong Xiao and Zhouping Xin. On the vanishing viscosity limit for the 3D Navier-Stokes equations with a slip boundary condition. Comm. Pure Appl. Math., 60(7):1027–1055, 2007.MathSciNetCrossRef
Metadaten
Titel
The Navier-Stokes Equations in a Curved Domain
verfasst von
Gung-Min Gie
Makram Hamouda
Chang-Yeol Jung
Roger M. Temam
Copyright-Jahr
2018
DOI
https://doi.org/10.1007/978-3-030-00638-9_7