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Boundary Layers for the Navier–Stokes Equations. The Case of a Characteristic Boundary
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Makram Hamouda
Published/Copyright:
March 10, 2010
Abstract
We prove the existence of a strong corrector for the linearized incompressible Navier–Stokes solution on a domain with characteristic boundary. This case is different from the noncharacteristic case considered in [Hamouda and Temam, Some singular perturbation problems related to the Navier–Stokes equations: Springer Verlag, 2006] and somehow physically more relevant. More precisely, we show that the linearized Navier–Stokes solutions behave like the Euler solutions except in a thin region, close to the boundary, where a certain heat equation solution is added (the corrector). Here, the Navier–Stokes equations are considered in an infinite channel of 
but our results still hold for more general bounded domains.
Key words and phrases:: Asymptotic expansions; boundary layer theory; heat equation; Navier–Stokes equations; singular perturbations
Received: 2008-03-12
Published Online: 2010-03-10
Published in Print: 2008-September
© Heldermann Verlag
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Keywords for this article
Asymptotic expansions;
boundary layer theory;
heat equation;
Navier–Stokes equations;
singular perturbations
Articles in the same Issue
- Higher Regularity of a Coupled Parabolic-Hyperbolic Fluid-Structure Interactive System
- Impulse Control in Discrete Time
- Mixed and Crack-Type Boundary Value Problems in Mindlin's Theory of Piezoelectricity
- Estimates of the Location of a Free Boundary for the Obstacle and Stefan Problems Obtained by Means of Some Energy Methods
- Extended Normal Vector Field and the Weingarten Map on Hypersurfaces
- Capacity Induced by a Nonlinear Operator and Applications
- Boundary Layers for the Navier–Stokes Equations. The Case of a Characteristic Boundary
- Large Time Behavior of Solutions to One Nonlinear Integro-Differential Equation
- On One Boundary Value Problem for a Nonlinear Equation with the Iterated Wave Operator in the Principal Part
- On Solvability and Well-Posedness of Boundary Value Problems for Nonlinear Hyperbolic Equations of the Fourth Order
- A Note on the One-Side Exact Boundary Observability for Quasilinear Hyperbolic Systems
- Principle of Exchange of Stabilities and Dynamic Transitions
