Regularitätsfragen für die instationären Navier-Stokesschen Gleichungen in höheren Dimensionen

Wolf VON WAHL

doi:10.2969/jmsj/03220263

Wolf VON WAHL

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1980 Volume 32 Issue 2 Pages 263-283

DOI https://doi.org/10.2969/jmsj/03220263

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Published: 1980 Received: June 21, 1978 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: October 20, 2006 Reason for correction: - Correction: TITLE Details: Wrong : Regularitätsfragen für die instationären Navier- Stokesschen Gleichungen in höheren Dimensionen
Right : Regularitätsfragen für die instationären Navier-Stokesschen Gleichungen in höheren Dimensionen

Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) S. Agmon, A. Douglis und L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions II, Comm. Pure Appl. Math., 17 (1964), 35-92.
2) A. Friedman, Partial Differential Equations, Holt, Rinehart and Winston, New York, San Francisco, Montreal, London, Sydney, 1969
3) E. Hopf, Über die Anfangswertaufgabe für die hydrodynamischen Grundgleichungen, Math. Nachrichten, 4 (1950/51), 213-231.
4) S. Kaniel und M. Shinbrot, Smoothness of weak solutions of the Navier-Stokes equations, Arch. Rational Mech. Anal., 24 (1967), 302-324.
5) J. L. Lions, Quelques Méthodes de Résolution des Problèmes nonlinéaires, Dunod, Paris, 1969.
6) O. A. Ladyzenskaja, Funktionalanalytische Untersuchungen der Navier-Stokesschen Gleichungen, Akademie-Verlag, Berlin, 1965.
7) O. A. Ladyzenskaja, V. A. Solonnikow und N. N. Ural'ceva, Linear and Quasilinear Equations of Parabolic Type, Translations of Mathematical Monographs, 23, American Mathematical Society, Providence, 1968.
8) V. A. Solonnikov, Estimates of the solutions of a nonstationary linearized system of Navier-Stokes equations, Amer. Math. Soc., Translations, Ser. 2, 75 (1968), 1-116 (translated from Trudy Mat. Inst. Steklov, 70 (1964), 213-317.)
9) V. A. Solonnikov und K. K. Golovkin, On the first boundaryvalue problem for nonstationary Navier-Stokes equations, Soviet Math. Dokl., 2 (1961), 1188-1191.
10) P. E. Sobolevskii, Study of Navier-Stokes equations by the methods of the theory of parabolic equations in Banach spaces, Soviet Math. Dokl., 5 (1964), 720-723.
11) J. Serrin, On the interior regularity of weak solutions of the Navier-Stokes equations, Arch. Rational Mech. Anal., 9 (1962), 187-195.
12) R. Témam, Navier-Stokes Equations, North-Holland Publishing Company, Amsterdam, New York, Oxford, 1977.
13) W. von Wahl, Instationary Navier-Stokes equations and parabolic systems, Pacific J. Math., 72 (1977), 557-569.

Right : [1] S. Agmon, A. Douglis und L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions II, Comm. Pure Appl. Math., 17 (1964), 35-92.
[2] A. Friedman, Partial Differential Equations, Holt, Rinehart and Winston, New York, San Francisco, Montreal, London, Sydney, 1969
[3] E. Hopf, Über die Anfangswertaufgabe für die hydrodynamischen Grundgleichungen, Math. Nachrichten, 4 (1950/51), 213-231.
[4] S. Kaniel und M. Shinbrot, Smoothness of weak solutions of the Navier-Stokes equations, Arch. Rational Mech. Anal., 24 (1967), 302-324.
[5] J. L. Lions, Quelques Méthodes de Résolution des Problèmes nonlinéaires, Dunod, Paris, 1969.
[6] O. A. Ladyzenskaja, Funktionalanalytische Untersuchungen der Navier-Stokesschen Gleichungen, Akademie-Verlag, Berlin, 1965.
[7] O. A. Ladyzenskaja, V. A. Solonnikow und N. N. Ural'ceva, Linear and Quasilinear Equations of Parabolic Type, Translations of Mathematical Monographs, 23, American Mathematical Society, Providence, 1968.
[8] V. A. Solonnikov, Estimates of the solutions of a nonstationary linearized system of Navier-Stokes equations, Amer. Math. Soc., Translations, Ser. 2, 75 (1968), 1-116 (translated from Trudy Mat. Inst. Steklov, 70 (1964), 213-317.)
[9] V. A. Solonnikov und K. K. Golovkin, On the first boundaryvalue problem for nonstationary Navier-Stokes equations, Soviet Math. Dokl., 2 (1961), 1188-1191.
[10] P. E. Sobolevskii, Study of Navier-Stokes equations by the methods of the theory of parabolic equations in Banach spaces, Soviet Math. Dokl., 5 (1964), 720-723.
[11] J. Serrin, On the interior regularity of weak solutions of the Navier-Stokes equations, Arch. Rational Mech. Anal., 9 (1962), 187-195.
[12] R. Témam, Navier-Stokes Equations, North-Holland Publishing Company, Amsterdam, New York, Oxford, 1977.
[13] W. von Wahl, Instationary Navier-Stokes equations and parabolic systems, Pacific J. Math., 72 (1977), 557-569.

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