On the stability of incompressible viscous fluid motions past objects

Kyûya MASUDA

doi:10.2969/jmsj/02720294

Kyûya MASUDA

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JOURNAL FREE ACCESS

1975 Volume 27 Issue 2 Pages 294-327

DOI https://doi.org/10.2969/jmsj/02720294

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Published: 1975 Received: June 12, 1974 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: CITATION Details: Wrong : 1) F. Odqvist, Über die Randwertaufgaben der Hydrodynamik zäher Flüssigkeiten, Math. Z., 32 (1930), 329-375.
2) J. Cannon and G. Knightly, Some continuous dependence theorems for viscous fluid motions, SIAM J. Appl. Math., 18 (1970), 627-641.
3) R. Finn, Stationary solutions of the Navier-Stokes equations, Proc. Symp. Appl. Math. 19 Amer. Math. Soc. (1965).
4) R. Finn, On the exterior stationary problem for the Navier-Stokes equations, and associated perturbation problems, Arch. Rational Mech. Anal., 19 (1965), 363-406.
5) H. Fujita and T. Kato, On the Navier-Stokes initial value problems. I, Arch. Rational Mech. Anal., 16 (1964) 269-315.
6) J. Heywood, On stationary solutions of the Navier-Stokes equations as limits of nonstationary solutions, Arch. Rational Mech. Anal., 37 (1970), 48-60.
7) T. Kato, A generalization of the Heinz inequality, Proc. Japan Acad., 37 (1961), 305-309.
8) A. Kiselev and O. Ladyzhenskaya, On the existence and uniqueness of non-compressible fluid, Izv. Akad. Nauk SSSR ser. Mat., 21 (1957), 655-680 (Amer. Math. Soc. Transl., (2) 24 (1963), 79-106).
9) O. Ladyzhenskaya, The mathematical theory of viscous incompressible flow, Gordon and Breach, New York, 1969.
10) G. Prodi, Un teorema di unicità per le equazioni di Navier-Stokes, Ann. Mat. Pura Appl. 48 (1959), 173-182.
11) J. Serrin, On the stability of viscous fluid motions, Arch. Rational Mech. Anal., 3 (1959), 1-13.
12) J. Serrin, The initial value problem for the Navier-Stokes equations, Proc. Symp. Nonlinear Problems (Madison, Wis., 1962) Univ. of Wisconsin Press, Madison, Wis., 1963, 69-98.
13) P. Sobolevski, On the non-stationary equations of the hydrodynamics of a viscous fluid, Dokl. Akad. Nauk SSSR, 128 (1959), 45-48.
14) W. Velte, Über emn stabilitatskriterium der Hydrodynamik, Arch. Rational Mech. Anal., 9 (1962), 9-20.
15) K. Yosida, Functional Analysis, Springer Verlag, Berlin-Heidelberg-New York 1966.
16) S. Krein, Linear Differential Equations in a Banach Space, Moskow, 1967 (in, Russian).
17) H. Weyl, Das asymptotische Verteilungsgesetz der Eigenschwingungen eines beliebig gestalteten elastischen Körpers, Rend. Circ. Mat. Palermo, 39 (1915), 1-50.
18) J. Heywood, The exterior nonstationary problem for the Navier-Stokes equations, Acta Math., 129 (1972), 11-34.
19) G. Knightly, On a class of global solutions of the Navier-Stokes equations, Arch. Rational Mech. Anal., 21 (1966), 211-245.
20) K. Masuda, On the analyticity and the unique continuation theorem for solutions of the Navier-Stokes equation, Proc. Japan Acad., 43 (1967), 827-832.

Right : [1] F. Odqvist, Über die Randwertaufgaben der Hydrodynamik zäher Flüssigkeiten, Math. Z., 32 (1930), 329-375.
[2] J. Cannon and G. Knightly, Some continuous dependence theorems for viscous fluid motions, SIAM J. Appl. Math., 18 (1970), 627-641.
[3] R. Finn, Stationary solutions of the Navier-Stokes equations, Proc. Symp. Appl. Math. 19 Amer. Math. Soc. (1965).
[4] R. Finn, On the exterior stationary problem for the Navier-Stokes equations, and associated perturbation problems, Arch. Rational Mech. Anal., 19 (1965), 363-406.
[5] H. Fujita and T. Kato, On the Navier-Stokes initial value problems. I, Arch. Rational Mech. Anal., 16 (1964) 269-315.
[6] J. Heywood, On stationary solutions of the Navier-Stokes equations as limits of nonstationary solutions, Arch. Rational Mech. Anal., 37 (1970), 48-60.
[7] T. Kato, A generalization of the Heinz inequality, Proc. Japan Acad., 37 (1961), 305-309.
[8] A. Kiselev and O. Ladyzhenskaya, On the existence and uniqueness of non-compressible fluid, Izv. Akad. Nauk SSSR ser. Mat., 21 (1957), 655-680 (Amer. Math. Soc. Transl., (2) 24 (1963), 79-106).
[9] O. Ladyzhenskaya, The mathematical theory of viscous incompressible flow, Gordon and Breach, New York, 1969.
[10] G. Prodi, Un teorema di unicità per le equazioni di Navier-Stokes, Ann. Mat. Pura Appl. 48 (1959), 173-182.
[11] J. Serrin, On the stability of viscous fluid motions, Arch. Rational Mech. Anal., 3 (1959), 1-13.
[12] J. Serrin, The initial value problem for the Navier-Stokes equations, Proc. Symp. Nonlinear Problems (Madison, Wis., 1962) Univ. of Wisconsin Press, Madison, Wis., 1963, 69-98.
[13] P. Sobolevski, On the non-stationary equations of the hydrodynamics of a viscous fluid, Dokl. Akad. Nauk SSSR, 128 (1959), 45-48.
[14] W. Velte, Über ein stabilitatskriterium der Hydrodynamik, Arch. Rational Mech. Anal., 9 (1962), 9-20.
[15] K. Yosida, Functional Analysis, Springer Verlag, Berlin-Heidelberg-New York 1966.
[16] S. Krein, Linear Differential Equations in a Banach Space, Moskow, 1967 (in, Russian).
[17] H. Weyl, Das asymptotische Verteilungsgesetz der Eigenschwingungen eines beliebig gestalteten elastischen Körpers, Rend. Circ. Mat. Palermo, 39 (1915), 1-50.
[18] J. Heywood, The exterior nonstationary problem for the Navier-Stokes equations, Acta Math., 129 (1972), 11-34.
[19] G. Knightly, On a class of global solutions of the Navier-Stokes equations, Arch. Rational Mech. Anal., 21 (1966), 211-245.
[20] K. Masuda, On the analyticity and the unique continuation theorem for solutions of the Navier-Stokes equation, Proc. Japan Acad., 43 (1967), 827-832.

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