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Some results on the asymptotic behavior of Hopf weak solutions to the Navier-Stokes equations in unbounded domains

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References

  1. Borchers, W., Miyakawa, T.:L 2 decay for the Navier-Stokes flow in Halfspaces. Math. Ann.282, 139–155 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  2. Caffarelli, L., Kohn, R., Nirenberg, L.: Partial regularity of suitable weak solutions of the Navier-Stokes equations. Commun. Pure Appl. Math.35, 771–832 (1982)

    MATH  MathSciNet  Google Scholar 

  3. Cattabriga, L.: Su un problema al contorno relativo al sistema di equationi di Stokes. Rend. Semin. Mat. Univ. Padova31, 308–340 (1961)

    MathSciNet  MATH  Google Scholar 

  4. Friedmann, A.: Partial differential equations, New York: Holt, Rinehart and Winston 1969

    Google Scholar 

  5. Galdi, G., Maremonti, P.: Monotonic decreasing and asymptotic behavior of the kinetic energy for weak solutions of the Navier-Stokes equations in exterior domains. Arch Ration. Mech. Anal.94, 253–266 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  6. Galdi, G.P., Rionero, S.: Weight energy methods in fluid dynamics and elasticity (Lect. Notes Math., vol. 1134) Berlin Heidelberg New York: Springer 1985

    Google Scholar 

  7. Galdi, G.P., Simader, C.G.: Existence, uniqueness andL a-estimates for the Stokes problem in an exterior domain (to appear)

  8. Giga, Y., Sohr, H.: On the Stokes operator in exterior domains. J. Fac. Sci. Univ. Tokyo36, 103–130 (1989)

    MathSciNet  Google Scholar 

  9. Heywood, J.G.: On nonstationary Stokes flow past an obstacle. Indiana Univ. Math. J.24, 271–284 (1974)

    Article  MATH  MathSciNet  Google Scholar 

  10. Heywood, J.G.: The Navier-Stokes equations: on the existence, regularity abd decay of solutions. Indiana Univ. Math. J.29, 639–681 (1980)

    Article  MATH  MathSciNet  Google Scholar 

  11. Heywood, J.C.: Epochs of regularity for weak solutions of the Navier-Stokes equations in unbounded domains. Tôhoku Math. J.40, 293–313 (1988)

    MATH  MathSciNet  Google Scholar 

  12. Hopf, E.: Über die Anfangswertaufgabe für die hydrodynamischen Grundgleichungen. Math. Nachr.4, 213–231 (1951)

    MATH  MathSciNet  Google Scholar 

  13. Kajikiva, R., Miyakawa, T.: OnL 2 decay of weak solutions of the Navier-Stokes equations inR n. Math. Z.192, 135–148 (1986)

    Article  MathSciNet  Google Scholar 

  14. Kato, T.:L p-solutions of the Navier-Stokes equation inR n. Math. Z.187, 471–480 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  15. Iwashita, H.:L q-Lp estimates for solutions of the nonstationary Stokes equations in an exterior domain and the Navier-Stokes initial value problems inL q space. Math. Ann.285, 265–288 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  16. Ladyzhenskaya, O.A.: The mathematical theory of viscous incompressible fluid. New York: Gordon Brech 1969

    Google Scholar 

  17. Leray, J.: Sur le mouvement d'un liquide visqueux emplissant l'espace. Acta Math.63, 193–248 (1934).

    Article  MATH  MathSciNet  Google Scholar 

  18. Maremonti, P.: Stabilità asintotica in media per moti fluidi viscosi in domini esterni. Ann. Mat. Pura Appl.142, 57–75 (1985)

    Article  MATH  Google Scholar 

  19. Maremonti, P.: Partial regularity of a generalized solution to the Navier-Stokes equations in exterior domains. Commun. Math. Phys.110, 75–87 (1987)

    Article  MATH  MathSciNet  Google Scholar 

  20. Maremonti, P.: On the asymptotic behavior of theL 2-norm of suitable weak solutions to the Navier-Stokes equations in three-dimensional exterior domains. Commun. Math. Phys.118, 385–400 (1988)

    Article  MATH  MathSciNet  Google Scholar 

  21. Maremonti, P.: Existence and stability of time periodic solutions to the Navier-Stokes equations in the whole space. Nonlinearity4, 503–529 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  22. Maremonti, P.: Some theorems of existence for solutions of the Navier-Stokes equations with slip boundary conditions in half-space. Ric. Mat. (in press)

  23. Maremonti, P., Russo, R.: On the existence and pointwise stability of periodic solutions to a linear parabolic equation in unbounded domains. Appl. Anal. (in press)

  24. Maremonti, P., Solonnikov, V.A.: An estimate for solutions of the Stokes equations in exterior domains (in Russian). Zap. Nauchn. Sernin. Leningr. Otd. Mat. Inst. Steklov.180, 105–120 (1990)

    Google Scholar 

  25. Masuda, K.: On the stability of incompressible viscous fluid motions past objects. J. Math. Soc. Japan27, 294–327 (1975)

    Article  MATH  MathSciNet  Google Scholar 

  26. Miranda, C.: Istituzioni di analisi funzionale lineare. Unione Mat. Ital. e. C.N.R. Tip. Oderisi Ed. Gubbio 1978

  27. Prodi, G.: Un teorema di unicita per le equazioni di Navier-Stokes. Ann. Mat. Pura Appl.48, 173–182 (1959)

    Article  MATH  MathSciNet  Google Scholar 

  28. Shonbek, M.E.:L 2-decay for weak solutions of the Navier-Stokes equations. Arch. Ration. Mech. Anal.89, 209–222 (1985)

    Article  Google Scholar 

  29. Shonbek, M.E.: Large time behaviour of solutions to the Navier-Stokes equations. Commun. Part. Differ. Equations11, 733–763 (1986)

    Google Scholar 

  30. Sohr, H., von Wahl, W.: On the regularity of the pressure of weak solutions of Navier-Stokes equations. Arch. Math.46, 428–439 (1986)

    Article  MATH  Google Scholar 

  31. Sohr, H., von Wahl, W., Wiegner, W.: Zur Asymptotik der Gleichungen von Navier-Stokes. Nachr. Akad. Wiss. Göttingen3, 45–59 (1986)

    Google Scholar 

  32. Solonnikov, V.A.: On estimates of Green's tensor for certain boundary problems. Dokl. Akad. Nauk SSSR130, 128–131 (1960)

    MathSciNet  Google Scholar 

  33. Solonnikov, V.A., Scadilov, V.E.: On a boundary value problem for a stationary system of Navier-Stokes equations. Proc. Steklov Inst. Math.125, 186–199 (1973)

    MATH  MathSciNet  Google Scholar 

  34. Vorovic, I.I., Judovic, V.I.: Steady flow of a viscous incompressible fluid. Mat. Sb.53, 393–428 (1961)

    MathSciNet  Google Scholar 

  35. Wiegner, W.: Decay results for weak solutions of the Navier-Stokes equations onR n. J. Lond. Math. Soc.35, 303–313 (1987)

    Article  MATH  MathSciNet  Google Scholar 

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  1. Dipartimento di Matematica, ”R. Caccioppoli”, Via Mezzocannone, 8, I-80134, Napoli, Italy

    Paolo Maremonti

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Maremonti, P. Some results on the asymptotic behavior of Hopf weak solutions to the Navier-Stokes equations in unbounded domains. Math Z 210, 1–22 (1992). https://doi.org/10.1007/BF02571780

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