On the asymptotic behavior of incompressible viscous fluid motions past bodies

Ryûichi MIZUMACHI

doi:10.2969/jmsj/03630497

Ryûichi MIZUMACHI

著者情報

ジャーナルフリー

1984 年 36 巻 3 号 p. 497-522

DOI https://doi.org/10.2969/jmsj/03630497

詳細

Published: 1984 Received: 1981/12/12 Available on J-STAGE: 2006/10/20 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/10/20 訂正理由: - 訂正箇所: 所属機関情報訂正内容: 訂正前 :
1) Mathematical Institute Tohoku University

訂正後 :
1) Mathematical Institute Tôhoku University

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) K. I. Babenko, On stationary solutions of the problem of flow past a body of a viscous incompressible fluid, Mat. Sbornik, 91(133) (1973), 3-26, (English transl. in Math. USSSR-Sb., 20 (1973), 1-25.)
2) K. I. Babenko and M. M. Vasil'ev, On the asymptotic behavior of a steady flow of viscous fluid at some distance from an immersed body, Prikl. Mat. Meh., 37 (1973), 690-705, (English transl. in J. Appl. Math. Mech., 37 (1973), 651-665).
3) D. Clark, The vorticity at infinity for solutions of the stationary Navier-Stokes equations in external domains, Indiana Univ. Math. J., 20(1971), 633-654.
4) R. Finn, On the steady state solutions of the Navier-Stokes equations III, Acta Math., 105 (1961), 197-244.
5) R. Finn, On the exterior stationary problem for the Navier-Stokes equations, and associated perturbation problems, Arch. Rational Mech. Anal., 19 (1965), 363-406.
6) R. Finn, Mathematical questions relating to viscous fluid flow in an exterior domain, Rocky Mt. J. Math., 3 (1973), 107-140.
7) H. Fujita and T. Kato, On the Navier-Stokes initial value problem 1, Arch. Rational Mech. Anal., 16 (1964), 269-315.
8) K. K. Golovkin and O. A. Ladyzenskaya, Solutions of non-stationary boundary value problems for Navier-Stokes equations, Trudy Mat. Inst. Steklov, 59 (1960), 100-114.
9) J. Heywood, The exterior nonstationary problem for the Navier-Stokes equations, Acta Math., 129 (1972), 11-34.
10) J. Heywood, The Navier-Stokes equations; On the existence, regularity and decay of solutions, Indiana Univ. Math. J., 29 (1980), 639-681.
11) E. Hopf, Über die Anfangswertaufgabe für die hydrodynamischen Grundgleichungen, Math. Nachr., 4 (1950-1951), 213-231.
12) G. Knightly, Some asymptotic properties of solutions of the Navier-Stokes equations, Dynamical systems, A. R. Bednarek and L. Cesari, eds., Academic Press, New York, 1977, 139-155.
13) G. Knightly, Some decay properties of solutions of the Navier-Stokes equations, Approximation methods for Navier-Stokes problems, R. Rautmann, ed., Lecture Notes in Math., 771, Springer, 1979, 287-298.
14) O. A. Ladyzenskaya, The mathematical theory of viscous incompressible flow, Gordon and Breach, New York, 1969.
15) J. Leray, Étude de diverses équations intégrales non linéaires et de quelques problèmes que pose l'hydrodynamique, J. Math. Pures Appl., Série 9, 12 (1933), 1-82.
16) P. I. Lizorkin, On multipliers of Fourier integrals in the space L_p,θ, Trudy Mat. Inst. Steklov, 89 (1967), 231-248, (English transl. in Proc. Steklov Inst. Math., 89 (1967), 269-290.)
17) K. Masuda, On the stability of incompressible viscous fluid motions past objects, J. Math. Soc. Japan, 27 (1975), 294-327.
18) K. Masuda, Non-stationary Navier-Stokes equations in the exterior domain, Functional analysis and numerical analysis, Japan-France seminar Tokyo and Kyoto, 1976, H. Fujita ed., Japan Society for the Promotion of Science, Tokyo, 1978, 267-275.
19) J. Serrin, On the interior regularity of weak solutions of the Navier-Stokes equations, Arch. Rational Mech. Anal., 9 (1962), 187-195.
20) V. A. Solonnikov, Estimates of the solutions of a nonstationary linearized system of Navier-Stokes equations, Trudy Mat. Inst. Steklov, 70 (1964), 213-317, (English transl. in Amer. Math. Soc. Transl., 75 (1968), 1-116).

Right : [1] K. I. Babenko, On stationary solutions of the problem of flow past a body of a viscous incompressible fluid, Mat. Sbornik, 91(133) (1973), 3-26, (English transl. in Math. USSSR-Sb., 20 (1973), 1-25.)
[2] K. I. Babenko and M. M. Vasil'ev, On the asymptotic behavior of a steady flow of viscous fluid at some distance from an immersed body, Prikl. Mat. Meh., 37 (1973), 690-705, (English transl. in J. Appl. Math. Mech., 37 (1973), 651-665).
[3] D. Clark, The vorticity at infinity for solutions of the stationary Navier-Stokes equations in external domains, Indiana Univ. Math. J., 20(1971), 633-654.
[4] R. Finn, On the steady state solutions of the Navier-Stokes equations III, Acta Math., 105 (1961), 197-244.
[5] R. Finn, On the exterior stationary problem for the Navier-Stokes equations, and associated perturbation problems, Arch. Rational Mech. Anal., 19 (1965), 363-406.
[6] R. Finn, Mathematical questions relating to viscous fluid flow in an exterior domain, Rocky Mt. J. Math., 3 (1973), 107-140.
[7] H. Fujita and T. Kato, On the Navier-Stokes initial value problem 1, Arch. Rational Mech. Anal., 16 (1964), 269-315.
[8] K. K. Golovkin and O. A. Ladyzenskaya, Solutions of non-stationary boundary value problems for Navier-Stokes equations, Trudy Mat. Inst. Steklov, 59 (1960), 100-114.
[9] J. Heywood, The exterior nonstationary problem for the Navier-Stokes equations, Acta Math., 129 (1972), 11-34.
[10] J. Heywood, The Navier-Stokes equations; On the existence, regularity and decay of solutions, Indiana Univ. Math. J., 29 (1980), 639-681.
[11] E. Hopf, Über die Anfangswertaufgabe für die hydrodynamischen Grundgleichungen, Math. Nachr., 4 (1950-1951), 213-231.
[12] G. Knightly, Some asymptotic properties of solutions of the Navier-Stokes equations, Dynamical systems, A. R. Bednarek and L. Cesari, eds., Academic Press, New York, 1977, 139-155.
[13] G. Knightly, Some decay properties of solutions of the Navier-Stokes equations, Approximation methods for Navier-Stokes problems, R. Rautmann, ed., Lecture Notes in Math., 771, Springer, 1979, 287-298.
[14] O. A. Ladyzenskaya, The mathematical theory of viscous incompressible flow, Gordon and Breach, New York, 1969.
[15] J. Leray, Étude de diverses équations intégrales non linéaires et de quelques problèmes que pose l'hydrodynamique, J. Math. Pures Appl., Série 9, 12 (1933), 1-82.
[16] P. I. Lizorkin, On multipliers of Fourier integrals in the space L_p,θ, Trudy Mat. Inst. Steklov, 89 (1967), 231-248, (English transl. in Proc. Steklov Inst. Math., 89 (1967), 269-290.)
[17] K. Masuda, On the stability of incompressible viscous fluid motions past objects, J. Math. Soc. Japan, 27 (1975), 294-327.
[18] K. Masuda, Non-stationary Navier-Stokes equations in the exterior domain, Functional analysis and numerical analysis, Japan-France seminar Tokyo and Kyoto, 1976, H. Fujita ed., Japan Society for the Promotion of Science, Tokyo, 1978, 267-275.
[19] J. Serrin, On the interior regularity of weak solutions of the Navier-Stokes equations, Arch. Rational Mech. Anal., 9 (1962), 187-195.
[20] V. A. Solonnikov, Estimates of the solutions of a nonstationary linearized system of Navier-Stokes equations, Trudy Mat. Inst. Steklov, 70 (1964), 213-317, (English transl. in Amer. Math. Soc. Transl., 75 (1968), 1-116).

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