Some application of the implicit function theorem to the stationary Navier-Stokes equations

• Autorzy: Konstanty Holly
• Języki publikacji: EN

Abstrakty

EN

We prove that - in the case of typical external forces - the set of stationary solutions of the Navier-Stokes equations is the limit of the (full) sequence of sets of solutions of the appropriate Galerkin equations, in the sense of the Hausdorff metric (for every inner approximation of the space of velocities). Then the uniqueness of the N-S equations is equivalent to the uniqueness of almost every of these Galerkin equations.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1991
• Tom: 54
• Numer: 2
• Strony: 93-109

Daty

wydano

1991

otrzymano

1989-01-18

poprawiono

1990-03-02

Twórcy

autor

Konstanty Holly

• Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland

Bibliografia

• [1] M. S. Berger, Nonlinearity and Functional Analysis, Benjamin, 1977.
• [2] M. G. Crandall and P. H. Rabinowitz, Bifurcation from simple eigenvalues, J. Funct. Anal. 8 (1971), p. 339.
• [3] C. Foiaş et J. C. Saut, Remarques sur les équations de Navier-Stokes stationnaires, Ann. Scuola Norm. Sup. Pisa (5) 1 (1983), p. 186.
• [4] C. Foiaş and R. Temam, Structure of the set of stationary solutions of the Navier-Stokes equations, Comm. Pure. Appl. Math. 30 (1977), 149-164.
• [5] J. L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod, Paris 1969.
• [6] K. Maurin, Analysis II, PWN, Warszawa 1980.
• [7] L. Nirenberg, Topics in Nonlinear Functional Analysis, Courant Institute, New York 1974.
• [8] W. Rudin, Functional Analysis, McGraw-Hill, New York 1973, Chap. 4.
• [9] J. C. Saut, Generic properties of nonlinear boundary value problems, in: Partial Differential Equations, Banach Center Publ. 10, PWN, Warszawa 1983, 331-351.
• [10] R. Temam, Navier-Stokes Equations, North-Holland, Amsterdam 1979.