Asymptotic analysis of Oseen type equations in a channel at small viscosity

Indiana University Mathematics Journal

Volumn 45, Issue 3, 1996, Pages 863-916

  Temam, Roger ^a,b   Wang, Xiaoming ^c,d  

^a INDIANA UNIVERSITY   (United States)

^b UNIVERSITÉ PARIS SACLAY   (France)

^c NEW YORK UNIVERSITY   (United States)

^d IOWA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001703051     PISSN: 00222518     EISSN: None     Source Type: Journal    
DOI: 10.1512/iumj.1996.45.1290     Document Type: Article

References (28)

1. R. BALIAN AND J. L. PEUBE, ED., Fluid dynamics, Cours de l'Ecole d'Eté de Physique Théorique, Les Houches, Gordon and Breach Science Publishers, New-York (1977).
2. G. K. BATCHELOR, An Introduction to Fluid Dynamics, Cambridge University Press, Cambridge (1967).
3. P. CONSTANTIN AND J. WU, Inviscid limit for vertex patches, Nonlinearity 8 (1995), 735-742.
4. M. CRANDALL, H. ISHII AND P. L. LIONS, User's Guide to Viscosity Solutions of Second Order Partial Differential Equations, Bull. Amer. Math. Soc. 27 no. 1 (July 1992), 1-67.
5. W. ECKHAUS, Asymptotic Analysis of Singular Perturbations, North-Holland (1979).
6. P. GERMAIN, Méthodes Asymptotiques en Mécanique des Fluides. In [1].
7. H. P. GREENSPAN, The Theory of Rotating Fluids, Cambridge Univ. Press, Cambridge (1968).
8. J. P. GUIRAUD, Focalisation dans les ondes courtes non linéaires, ONERA T.P. 686, (1969).
9. 3, J. Funct. Anal. 9 (1972), 296-305.
10. O. A. LADYZHENSKAYA, The mathematical theory of viscous incompressible flows, 2nd ed, Gordon and Breach, New York, (1969).
11. P. LAGERSTRÖM, Matched Asymptotics Expansion, Ideas and Techniques, Springer-Verlag, New York, (1988).
12. H. LAMB, Hydrodynamics, reprinted by Dover, New-York, (1945).
13. L. LANDAU AND E. LIFSCHITZ, Fluid Mechanics, Addison-Wesley, New York, (1953).
14. J. L. LIONS, Perturbations singulières dans les problèmes aux limites et en controle optimal, Lecture Notes in Math 323, Springer-Verlag, New York, (1973).
15. O. OLEINIK, The Prandtl system of equations in boundary layer theory, Dokl. Akad. Nauk S.S.S.R. 150 4(3) (1963), 583-586.
16. H. K. MOFFATT, Six lectures on general fluid dynamics and two on hydromagnetic dynamo theory. In [1].
17. L. PRANDTL, Veber Flüssigkeiten bei sehr kleiner Reibung, Verh. III Intern. Math Kongr. Heidelberg (1905), 484-491, Teuber, Leibzig.
18. L. ROSENHEAD, Laminar boundary layers; an account of the development, structure, and stability of laminar boundary layers in incompressible fluids, together with a description of the associated experimental techniques, Oxford Clarendon Press, (1963).
19. R. TEMAM, Navier-Stokes Equations 4th Edition, North-Holland, Amsterdam, (1977).
20. R. TEMAM, Infinite Dimensional Dynamical Systems in Mechanics and Physics, Springer-Verlag, New York, Berlin, (1988).
21. R. TEMAM, Behavior at time t = 0 of the solutions of semilinear evolution equations, J. Diff. Equations, 43 (1982), 73-92.
22. R. TEMAM AND X. WANG, Asymptotic Analysis of the Linearized Navier-Stokes Equations in a Channel, Differential & Integral Equations 8 no. 7, (1995), 1591-1618.
23. M. VAN DYKE, Perturbation methods in fluid mechanics, Academic Press, New York.
24. M. I. VISHIK AND L. A. LYUSTERNIK, Regular degeneration and boundary layer for linear differential equations with small parameter, Uspekki Mat. Nauk, 12 (1957), 3-122.
25. T. YANAGISAWA AND Z. XIN, Singular perturbation of Euler equations with characteristic boundary condition, in preparation..
26. K. YOSIDA, Functional Analysis, Springer-Verlag, New York, (1965).
27. S.N. ALEKSEENKO, Existence and asymptotic representation of weak solutions to the flowing problem under the condition of regular slippage on solid walls, Siberian Math. Journ. 35 no. 2 (1994), 209-229.
28. R. TEMAM AND X. WANG, article in preparation.