36
Views
0
CrossRef citations to date
0
Altmetric
Original Articles

On the stability phenomenon of the Navier-Stokes type equations for elliptic complexes

&
Pages 1122-1150 | Received 06 Jun 2020, Accepted 06 Oct 2020, Published online: 03 Nov 2020

References

  • Leray J. Essai sur les mouvements plans d'un liquid visqueux que limitend des parois. J Math Pures Appl. 1934;9:331–418.
  • Leray J. Sur le mouvement plans d'un liquid visqueux emplissant l'espace. Acta Math. 1934;63:193–248.
  • Kolmogorov AN. Equations of turbulent mouvement of incompressible fluid. Izv AN SSSR Phys Ser. 1942;6(1):56–58. Russian.
  • Hopf E. Über die Anfangswertaufgabe für die hydrodynamischen Grundgleichungen. Math Nachr. 1951;4:213–231.
  • Ladyzhenskaya OA. Mathematical problems of incompressible viscous fluid. Moscow: Nauka; 1970. 288 pp. Russian.
  • Fursikov AV, Vishik MI. Mathematical problems of statistical hydrodynamics. Moscow: Nauka; 1980. 440 pp. Russian.
  • Gallagher I. Remarks on the global regularity for solutions to the incompressible Navier-Stokes equations. Zürich: European Mathematical Society; 2013. p. 331–345. (European Congress of Mathematics).
  • Shlapunov A, Tarkhanov N. An open mapping theorem for the Navier-Stokes equations. Adv Appl Fluid Mech. 2018;21(2):127–246.
  • Mera A, Tarkhanov N, Shlapunov AA. Navier-Stokes equations for elliptic complexes. J Siberian Federal Univ Math Phys. 2019;12(1):3–27.
  • Tarkhanov N. Complexes of differential operators. Dordrecht (NL): Kluwer Academic Publishers; 1995.
  • Nicolaescu LI. Lectures on the geometry of manifolds. London: World Scientific; 2007.
  • Eidelman SD. Parabolic equations. Partial differential equations 6. Moscow: VINITI; 1990. p. 201–313. (Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Fund. Napr.; vol. 63). Russian.
  • Landau LD, Lifshitz EM. Fluid mechanics. London: Pergamon Press; 1959. (A course of theoretical physics; vol. 6).
  • Temam R. Navier-Stokes equations and nonlinear functional analysis. 2nd ed. Philadelphia: SIAM; 1995.
  • Ebin DG, Marsden J. Groups of diffeormophisms and the motion of an incompressible fluid. Ann Math. 1970;92:102–163.
  • Taylor M. Partial differential equations III: non-linear equations. New York: Springer-Verlag; 2010.
  • Chan CH, Czubak M. Non-uniqueness of the Leray-Hopf solutions in the hyperbolic setting. Dyn Part Differ Eq. 2013;10(1):43–77.
  • Lichtenfelz LA. Nonuniqueness of solutions of the Navier-Stokes equations on Riemannian manifolds. Ann Global Anal Geom. 2016;50(3):237–248.
  • Ladyzhenskaya OA, Solonnikov VA, Ural'tseva NN. Linear and quasilinear equations of parabolic type. Moscow: Nauka; 1967. Russian.
  • Gilbarg D, Trudinger N. Elliptic partial differential equations of second order. Berlin: Springer-Verlag; 1983.
  • Eidelman SD. On fundamental solutions of parabolic equations. Mat Sb. 1956;38(80)(1):51–92. Russian.
  • Friedman A. Partial differential equations of parabolic type. Englewood Cliffs (NJ): Prentice-Hall; 1964.
  • Temam R. Navier-Stokes equations. Theory and numerical analysis. Amsterdam: North Holland; 1979.
  • Smale S. An infinite dimensional version of Sard's theorem. Am J Math. 1965;87(4), 861–866.
  • Hamilton RS. The inverse function theorem of Nash and Moser. Bull AMS. 1982;7(1):65–223.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.