This is a preview of subscription content, log in via an institution to check access.
Literature cited
E. Hopf, “A mathematical example displaying features of turbulence,” Commun. Pure Appl. Math.,1, 303–322 (1948).
C. Foias and G. Prodi, “Sur le comportement global des solutions nonstationaires des equations de Navier-Stokes en dimension 2,” Rend. Semin. Matem. Univ. Padova,39, 1–34 (1967).
O. A. Ladyzhenskaya, Mathematical Aspects of Viscous Incompressible Fluid Dynamics [in Russian], Nauka, Moscow (1970).
O. A. Ladyzhenskaya, “Integral estimates, the convergence of approximative methods, and solutions in functionals for linear elliptic operators,” Vest. Leningrad. Gos. Univ., No. 7, 60–69 (1958).
V. V. Nemytskii and V. V. Stepanov, Qualitative Theory of Differential Equations [in Russian], GITTL, Moscow (1949).
S. G. Krein, “Correctness classes for certain boundary-value problems,” Dokl. Akad. Nauk SSSR,114, No. 6, 1162–1165 (1957).
P. J. Cohen and M. Lees, “Asymptotic decay of solutions of differential inequalities,” Pacific J. Math.,11, 1235–1249 (1961).
S. Agmon and L. Nirenberg, “Properties of solutions of ordinary differential equations in Banach space,” Commun. Pure Appl. Math.,16, 121–239 (1963).
H. Ogawa, “Lower bounds for solutions of differential inequalities in Hilbert space,” Proc. Amer. Math. Soc.,16, No. 6, 1241–1243 (1965).
V. I. Yudovich, “Remark on the stationary solutions of the Navier-Stokes equations,” in: Mathematical Analysis and Its Applications [in Russian], Izd. Rostov. Gos. Univ., Rostov-on-Don (1969), pp. 190–194.
Additional information
Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova Akademii Nauk SSSR, Vol. 27, pp. 91–115, 1972.
Rights and permissions
About this article
Cite this article
Ladyzhenskaya, O.A. A dynamical system generated by the Navier-Stokes equations. J Math Sci 3, 458–479 (1975). https://doi.org/10.1007/BF01084684
Issue Date:
DOI: https://doi.org/10.1007/BF01084684