Steady solutions of the Navier-Stokes equations in unbounded channels and pipes

 Access to full text

 Full (PDF)

1. [1] J. Leray, Étude de diverses équations intégrales non linéares et de quelques problèmes que pose l'Hydrodynamique, J. Math. Pures Appl. (ser. 9), 12 (1933), pp. 1-82. Zbl0006.16702JFM59.0402.01
2. [2] O.A. Ladyzhenskaya, The mathematical theory of viscous incompressible flow, Gordon and Breach, London -New York, 1963. Zbl0121.42701MR155093
3. [3] R. Finn, Stationary solutions of the Navier-Stokes equations, Amer. Math. Soc., Proc. Symposia Appl. Math., 17 (1965), pp. 121-153. Zbl0148.21602
4. [4] R. Finn, Mathematical questions relating to viscous fluid flow in an exterior domain, Rocky Mountain Journal of Math., 3, no. 1 (1973), pp. 107-140. Zbl0261.35068MR327146
5. [5] L.E. Fraenkel, On a theory of laminar flow in channels of a certain class, Proc. Camb. Phil. Soc., 73 (1973), pp. 361-390. Zbl0265.76039MR311198
6. [6] L.E. Fraenkel - P.M. Eagles, On a theory of laminar flow in channels of a certain class II, Math. Proc. Camb. Phil. Soc., 77 (1975), pp. 199-224. MR359533
7. [7] O.A. Ladyzhenskaya, Stationary motion of a viscous incompressible fluid in a pipe, Dokl. Akad. Nauk. SSSR, 124 (1959), pp. 551-553. Zbl0096.41302MR106641
8. [8] L.E. Fraenkel, Boundary-value problems for the steady Navier-Stokes equations, Zeitschr. Angew. Math. Mech. (to appear in the issue reporting the 1975Jahrestagung of the Gesellscheft Angew. Math. Mech.). Zbl0331.35051MR492969
9. [9] S.L. Sobolev, Applications of functional analysis in mathematical physics, Amer. Math. Soc., Providence, Rhode Island, 1963. Zbl0123.09003MR165337
10. [10] G.H. Hardy - J.E. Littlewood - G. Polya, Inequalities, Cambridge University Press, London-New York, 1952. Zbl0047.05302MR46395
11. [11] F. Treves, Basic linear partial differential equations, Academic Press, New York, 1975. Zbl0305.35001MR447753
12. [12] J.L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéares, Dunod, Paris, 1969. Zbl0189.40603MR259693
13. [13] J. Heywood, On uniqueness questions in the theory of viscous flow, Acta Math.136 (1976), pp. 61-102. Zbl0347.76016MR425390
14. [14] H. Fujita, On the existence and regularity of the steady-state solutions of the Navier-Stokes equations, J. Fac. Sci. Univ. Tokyo Sect. I, 9 (1961), pp. 59-102. Zbl0111.38502MR132307
15. [15] R. Finn, On the steady-state solutions of the Navier-Stokes equations, III, Acta Math., 105 (1961), pp. 197-244. Zbl0126.42203MR166498
16. [16] L.E. Fraenkel, Lectures on fixed-point theorems and their application, Univ. of Cambridge (1973). 
17. [17] J. Serrin, On the stability of viscous fluid motions, Arch. Rat. Mech. Anal.3 (1959), pp. 1-13. Zbl0086.20001MR105250
18. [18] A. Friedman, Partial differential equations, Holt, Rinehart and Winston, New York, 1969. Zbl0224.35002MR445088
19. [19] L. Nirenberg, On elliptic partial differential equations, Ann. Scuola Norm. Sup. Pisa, 13 (1959), pp. 115-162. Zbl0088.07601MR109940

1. S. A. Nazarov, K. Pileckas, Asymptotics of solutions to Stokes and Navier-Stokes equations in domains with paraboloidal outlets to infinity
2. K. Pileckas, Strong solutions of the steady nonlinear Navier-Stokes system in domains with exits to infinity