The Navier-Stokes equations and the maximum principle

International Mathematics Research Notices

Volumn , Issue 67, 2004, Pages 3585-3605

  Mucha, Piotr Bogusław ^a  

^a UNIVERSITY OF WARSAW   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 21244452703     PISSN: 10737928     EISSN: None     Source Type: Journal    
DOI: 10.1155/s1073792804133345     Document Type: Article

References (16)

1. C. J. Amick and L. E. Fraenkel, Steady solutions of the Navier-Stokes equations representing plane flow in channels of various types, Acta Math. 144 (1980), no. 1-2, 83-151.
2. T. Clopeau, A. Mikelić, and R. Robert, On the vanishing viscosity limit for the 2D incompressible Navier-Stokes equations with the friction type boundary conditions, Nonlinearity 11 (1998), no. 6, 1625-1636.
3. R. Farwig, Stationary solutions of compressible Navier-Stokes equations with slip boundary condition, Comm. Partial Differential Equations 14 (1989), no. 11, 1579-1606.
4. M. A. Fontelos and A. Friedman, Stationary non-Newtonian fluid flows in channel-like and pipe-like domains, Arch. Ration. Mech. Anal. 151 (2000), no. 1, 1-43.
5. G. P. Galdi, An Introduction to the Mathematical Theory of the Navier-Stokes Equations. Vol. I. Linearized Steady Problems, Springer Tracts in Natural Philosophy, vol. 38, Springer, New York, 1994.
6. _, An Introduction to the Mathematical Theory of the Navier-Stokes Equations. Vol. II. Nonlinear Steady Problems, Springer Tracts in Natural Philosophy, vol. 39, Springer, New York, 1994.
7. Y. Giga, S. Matsui, and O. Sawada, Global existence of two-dimensional Navier-Stokes flow with nondecaying initial velocity, J. Math. Fluid Mech. 3 (2001), no. 3, 302-315.
8. T. Kato and H. Fujita, Maximum principle for vorticity in viscous fluid, J. Phys. Soc. Japan 14 (1959), 545.
9. O. A. Ladyženskaja and V. A. Solonnikov, Determination of solutions of boundary value problems for stationary Stokes and Navier-Stokes equations having an unbounded Dirichlet integral, Zap. Nauchn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) 96 (1980), 117-160 (Russian).
10. O. A. Ladyzhenskaya, The Mathematical Theory of Viscous Incompressible Flow, Gordon and Breach Science Publishers, New York, 1963.
11. P. B. Mucha, On the inviscid limit of the Navier-Stokes equations for flows with large flux, Nonlinearity 16 (2003), no. 5, 1715-1732.
12. _, On a problem for the Navier-Stokes equations with the infinite Dirichlet integral, to appear in Z. Angew. Math. Phys.
13. V. A. Solonnikov and V. E. Scadilov, On a boundary value problem for a stationary system of Navier-Stokes equations, Trudy Mat. Inst. Steklov. 125 (1973), 196-210.
14. A. Tani, S. Itoh, and N. Tanaka, The initial value problem for the Navier-Stokes equations with general slip boundary condition, Adv. Math. Sci. Appl. 4 (1994), no. 1, 51-69.
15. R. Temam, Navier-Stokes Equations. Theory and Numerical Analysis, Studies in Mathematics and Its Applications, vol. 2, North-Holland Publishing, Amsterdam, 1977.
16. W. M. Zajaczkowski, On global special solutions for Navier-Stokes equations with boundary slip condition in a cylindrical domain, to appear in GAKUTO Internat. Ser. Math. Sci. Appl.