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The exterior non-stationary problem for the Navier-Stokes equations in regions with moving boundaries
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1990 Volume 42 Issue 3 Pages 495-509
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- Published: 1990 Received: February 06, 1989 Available on J-STAGE: October 20, 2006 Accepted: - Advance online publication: - Revised: -
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Correction information
Date of correction: October 20, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) H. Fujita and N. Sauer, On existence of weak solutions of the Navier-Stokes in regions with moving boundary, J. Fac. Sci. Univ. Tokyo Sect. IA Math., 17 (1970), 403-420.
2) G. P. Galdi and P. Maremonti, Monotonic decreasing and asymptotic behavior of the kinetic energy for weak solutions of the Navier-Stokes equations in exterior domains, Arch. Rational Mech. Anal., 94 (1986), 253-266.
3) V. Giraut and P. A. Raviart, Finite element approximation of the Navier-Stokes equations, Lecture Notes in Math., 749, Springer, 1979.
4) J. G. Heywood, The exterior nonstationary problem for the Navier-Stokes equations, Acta Math., 129 (1972), 11-34.
5) J. G. Heywood, A uniqueness theorem for non stationary Navier-Stokes flow past an obstacle, Ann. Scuola Norm. Sup. Pisa Cl. Sci., 6 (1979), 427-445.
6) J. G. Heywood, The Navier-Stokes equations: On the existence, regularity and decay of solutions, Indiana Univ. Math. J., 29 (1980), 639-681.
7) A. Inoue and M. Wakimoto, On existence of solutions of the Navier-Stokes equations in a time dependent domain, J. Fac. Sci. Univ. Tokyo Sect. IA Math., 24 (1977), 303-319.
8) O. A. Ladyzhenskaya, The mathematical theory of viscous incompressible flow, Gordon & Breach, New York, 1969.
9) J. Leray, Sur le movement d'un liquide visqueux emplissant l'espace, Acta Math., 63 (1934), 193-248.
10) J. L. Lions, Singular pertubation and some nonlinear boundary value problems, MRC Tech. Summary Rep., 421, 1963.
11) K. Masuda, On the stability of incompressible viscous fluid motion past objects, J. Math. Soc. Japan, 27 (1975), 294-327.
12) T. Miyakawa and H. Sohr, On energy inequality, smoothness and large time behavior in L2 for weak solutions of the Navier-Stokes equations in exterior domains, Math. Z., 199 (1988), 455-478.
13) H. Morimoto, On existence of periodic weak solutions of the Navier-Stokes equations in regions with periodically moving boundaries, J. Fac. Sci. Univ. Tokyo Sect. IA Math., 18 (1971), 499-524.
14) T. Miyakawa and Y. Teramoto, Existence and periodicity of weak solutions of the Navier-Stokes equations in a time dependent domain, Hiroshima Math. J., 12 (1982), 513-528.
15) D. Nye Bock, On the Navier-Stokes equations in non cylindrical domains, Thesis, University of Maryland.
16) M. Otani and Y. Yamada, On the Navier-Stokes equations in a non cylindrical domains: An approach by subdifferential operator theory, J. Fac. Sci. Univ. Tokyo Sect. IA Math., 25 (1978), 185-204.
17) R. Salvi, On the existence of weak solutions of a non-linear mixed problem for the Navier-Stokes equations, J. Fac. Sci. Univ. Tokyo Sect. IA Math., 32 (1985), 213-221.
18) R. Salvi, On the existence of weak solutions of a non-linear mixed problem for non homogeneous fluids in a time dependent domain, C. M. U. C., 26 (1985), 185-199.
19) R. Salvi, On the existence of periodic weak solutions of the Navier-Stokes equations in regions with periodically moving boundaries, preprint.
20) R. Salvi, On the Navier-Stokes equations in non cylindrical domains: On the existence and regularity, Math. Z., 199 (1988), 153-170.
21) H. Sohr, W. von Wahl and M. Wiegner, Zur asymptotik der gleichungn von Navier-Stokes, preprint.
22) R. Temam, Navier-Stokes equations, North-Holland, 1977.
23) Y. Teramoto, On the stability of periodic solutions of the Navier-Stokes equations in a non-cylindrical domain, Hiroshima Math. J., 13 (1983), 457-467.
24) Y. Teramoto, On asymptotic behavior of solutions for the Navier-Stokes equations in a time dependent domain, Math. Z., 186 (1984), 29-40.
25) F. Treves, Basic linear partial differential equations, Academic Press, 1975.
Right : [1] H. Fujita and N. Sauer, On existence of weak solutions of the Navier-Stokes in regions with moving boundary, J. Fac. Sci. Univ. Tokyo Sect. IA Math., 17 (1970), 403-420.
[2] G. P. Galdi and P. Maremonti, Monotonic decreasing and asymptotic behavior of the kinetic energy for weak solutions of the Navier-Stokes equations in exterior domains, Arch. Rational Mech. Anal., 94 (1986), 253-266.
[3] V. Giraut and P. A. Raviart, Finite element approximation of the Navier-Stokes equations, Lecture Notes in Math., 749, Springer, 1979.
[4] J. G. Heywood, The exterior nonstationary problem for the Navier-Stokes equations, Acta Math., 129 (1972), 11-34.
[5] J. G. Heywood, A uniqueness theorem for non stationary Navier-Stokes flow past an obstacle, Ann. Scuola Norm. Sup. Pisa Cl. Sci., 6 (1979), 427-445.
[6] J. G. Heywood, The Navier-Stokes equations: On the existence, regularity and decay of solutions, Indiana Univ. Math. J., 29 (1980), 639-681.
[7] A. Inoue and M. Wakimoto, On existence of solutions of the Navier-Stokes equations in a time dependent domain, J. Fac. Sci. Univ. Tokyo Sect. IA Math., 24 (1977), 303-319.
[8] O. A. Ladyzhenskaya, The mathematical theory of viscous incompressible flow, Gordon & Breach, New York, 1969.
[9] J. Leray, Sur le movement d'un liquide visqueux emplissant l'espace, Acta Math., 63 (1934), 193-248.
[10] J. L. Lions, Singular pertubation and some nonlinear boundary value problems, MRC Tech. Summary Rep., 421, 1963.
[11] K. Masuda, On the stability of incompressible viscous fluid motion past objects, J. Math. Soc. Japan, 27 (1975), 294-327.
[12] T. Miyakawa and H. Sohr, On energy inequality, smoothness and large time behavior in L2 for weak solutions of the Navier-Stokes equations in exterior domains, Math. Z., 199 (1988), 455-478.
[13] H. Morimoto, On existence of periodic weak solutions of the Navier-Stokes equations in regions with periodically moving boundaries, J. Fac. Sci. Univ. Tokyo Sect. IA Math., 18 (1971), 499-524.
[14] T. Miyakawa and Y. Teramoto, Existence and periodicity of weak solutions of the Navier-Stokes equations in a time dependent domain, Hiroshima Math. J., 12 (1982), 513-528.
[15] D. Nye Bock, On the Navier-Stokes equations in non cylindrical domains, Thesis, University of Maryland.
[16] M. Otani and Y. Yamada, On the Navier-Stokes equations in a non cylindrical domains: An approach by subdifferential operator theory, J. Fac. Sci. Univ. Tokyo Sect. IA Math., 25 (1978), 185-204.
[17] R. Salvi, On the existence of weak solutions of a non-linear mixed problem for the Navier-Stokes equations, J. Fac. Sci. Univ. Tokyo Sect. IA Math., 32 (1985), 213-221.
[18] R. Salvi, On the existence of weak solutions of a non-linear mixed problem for non homogeneous fluids in a time dependent domain, C. M. U. C., 26 (1985), 185-199.
[19] R. Salvi, On the existence of periodic weak solutions of the Navier-Stokes equations in regions with periodically moving boundaries, preprint.
[20] R. Salvi, On the Navier-Stokes equations in non cylindrical domains: On the existence and regularity, Math. Z., 199 (1988), 153-170.
[21] H. Sohr, W. von Wahl and M. Wiegner, Zur asymptotik der gleichungn von Navier-Stokes, preprint.
[22] R. Temam, Navier-Stokes equations, North-Holland, 1977.
[23] Y. Teramoto, On the stability of periodic solutions of the Navier-Stokes equations in a non-cylindrical domain, Hiroshima Math. J., 13 (1983), 457-467.
[24] Y. Teramoto, On asymptotic behavior of solutions for the Navier-Stokes equations in a time dependent domain, Math. Z., 186 (1984), 29-40.
[25] F. Treves, Basic linear partial differential equations, Academic Press, 1975.
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