Article PDF
Avoid common mistakes on your manuscript.
References
Babenko, K. I., On stationary solutions of the problem of flow past a body of viscous incompressible fluid. Math. USSR-Sb. 20, 1–25 (1973).
Borchers, W.,& Miyakawa, T., L 2decay for the Navier-Stokes flow in halfspaces. Math. Ann. 282, 139–155 (1988).
Borchers, W., & Miyakawa, T., Algebraic L 2 decay for Navier-Stokes flows in exterior domains. Acta Math. 165, 189–227 (1990).
Finn, R., On the exterior stationary problem for the Navier-Stokes equations, and associated perturbation problems. Arch. Rational Mech. Anal. 19, 363–406 (1965).
Finn, R., Mathematical questions relating to viscous fluid flow in an exterior domain. Rocky Mountain J. Math. 3, 107–140 (1973).
Galdi, G. P., & Rionero, S., Weighted Energy Methods in Fluid Dynamics and Elasticity. Lecture Notes in Math. 1134, Berlin-Heidelberg-New York: Springer-Verlag 1985.
Giga, Y., & Miyakawa, T., Navier-Stokes flow in R 3 with measures as initial vorticity and Morrey spaces. Commun. in Partial Diff. Eq. 14, 577–618 (1989).
Heywood, J. G., On stationary solutions of the Navier-Stokes equations as limits of nonstationary solutions. Arch. Rational Mech. Anal. 37, 48–60 (1970).
Heywood, J. G., The exterior nonstationary problem for the Navier-Stokes equations. Acta Math. 129, 11–34 (1972).
Heywood, J. G., The Navier-Stokes equations: On the existence, regularity and decay of solutions. Indiana Univ. Math. J. 29, 639–681 (1980).
Janson, S., & Jones, P. W., Interpolation between H pspaces: the complex method. J. Funct. Anal. 48, 58–80 (1982).
Kajikiya, R., & Miyakawa, T., On L 2 decay of weak solutions of the NavierStokes equations in R m.Math. Z. 192, 135–148 (1986).
Kato, T., Strong L psolutions of the Navier-Stokes equation in R m,with applications to weak solutions. Math. Z. 187, 471–480 (1984).
Leray, J., Sur le mouvement d'un liquide visqueux emplissant l'espace. Acta Math. 63, 193–248 (1934).
Masuda, K., On the stability of incompressible viscous fluid motions past objects. J. Math. Soc. Japan 27, 294–327 (1975).
Masuda, K., Weak solutions of the Navier-Stokes equations. Tôhoku Math. J. 36, 623–646 (1984).
Miyakawa, T., On nonstationary solutions of the Navier-Stokes equations in an exterior domain. Hiroshima Math. J. 12, 115–140 (1982).
Miyakawa, T., & Sohr, H., On energy inequality, smoothness and large time behavior in L2 for weak solutions of the Navier-Stokes equations in exterior domains. Math. Z. 199, 455–478 (1988).
Reed, M., & Simon, B., Methods of Modern Mathematical Physics, Vol. II; Fourier Analysis, Self-Adjointness. New York: Academic Press 1975.
Schonbek, M. E., L 2 decay for weak solutions of the Navier-Stokes equations. Arch. Rational Mech. Anal. 88, 209–222 (1985).
Schonbek, M. E., Large time behaviour of solutions to the Navier-Stokes equations. Commun. in Partial Diff. Eq. 11, 733–763 (1986).
Temam, R., Navier-Stokes Equations. Amsterdam: North-Holland 1977.
Wiegner, M., Decay results for weak solutions of the Navier-Stokes equations in R n.J. London Math. Soc. 35, 303–313 (1987).
Borchers, W., & Miyakawa, T., On large time behavior of the total kinetic energy for weak solutions of the Navier-Stokes equations in unbounded domains. Proc. of a symposium on the Navier-Stokes equations, Oberwolfach 1988; to appear in Lecture Notes in Math., Berlin-Heidelberg-New York: Springer-Verlag.
Author information
Authors and Affiliations
Additional information
Communicated by C. Dafermos
Rights and permissions
About this article
Cite this article
Borchers, W., Miyakawa, T. L2-decay for Navier-Stokes flows in unbounded domains, with application to exterior stationary flows. Arch. Rational Mech. Anal. 118, 273–295 (1992). https://doi.org/10.1007/BF00387899
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00387899