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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ジャーナルフリー

1980 年 32 巻 2 号 p. 263-283

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

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Published: 1980 Received: 1978/06/21 Available on J-STAGE: 2006/10/20 Accepted: - Advance online publication: - Revised: -
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訂正日: 2006/10/20 訂正理由: - 訂正箇所: 論文タイトル訂正内容: Wrong : Regularitätsfragen für die instationären Navier- Stokesschen Gleichungen in höheren Dimensionen
Right : Regularitätsfragen für die instationären Navier-Stokesschen Gleichungen in höheren Dimensionen

訂正日: 2006/10/20 訂正理由: - 訂正箇所: 引用文献情報訂正内容: 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.

訂正日: 2006/10/20 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

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