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Survey on time periodic problem for fluid flow under inhomogeneous boundary condition
1. | Department of Mathematics, Meiji University, Kawasaki, 214-8571, Japan |
References:
[1] |
C. J. Amick, Existence of solutions to the nonhomogeneous steady Navier-Stokes equations,, Indiana Univ. Math. J., 33 (1984), 817.
doi: 10.1512/iumj.1984.33.33043. |
[2] |
R. Farwig and H. Morimoto, Leray's inequality for fluid flow in symmetric multi-connected doamins,, Darmstadt University of Technology, 2612 (2010). Google Scholar |
[3] |
H. Fujita, On the existence and regularity of the steady-state solutions of the Navier-Stokes theorem,, J. Fac. Sci. Univ. Tokyo, 9 (1961), 59.
|
[4] |
H. Fujita, On stationary solutions to Navier-Stokes equations in symmetric plane domains under general outflow condition,, in, 388 (1998), 16.
|
[5] |
G. P. Galdi, "An Introduction to the Mathematical Theory of the Navier-Stokes Equations. Vol. II, Nonlinear Steady Problems,", Springer Tracts in Natural Philosophy, 39 (1994).
|
[6] |
E. Hopf, Ein allgemeiner Endlichkeitssatz der Hydrodynamik,, Math. Ann., 117 (1941), 764.
doi: 10.1007/BF01450040. |
[7] |
E. Hopf, "On Nonlinear Partial Differential Equations,", Lecture Series of the Symposium on Partial Differential Equations, (1957), 1. Google Scholar |
[8] |
H. Inoue and M. Ôtani, Periodic Problems for Heat Convection Equations in Noncylindrical Domains,, Funkcialaj Ekvacioj, 40 (1997), 19.
|
[9] |
S. Kaniel and M. Shinbrot, A reproductive property of the Navier-Stokes eqautions,, Arch. Rat. Mech. Anal., 24 (1967), 363.
doi: 10.1007/BF00253153. |
[10] |
T-P. Kobayashi, Time periodic solutions of the Navier-Stokes equations under general outflow condition,, Tokyo Journal of Mathematics, 32 (2009), 409.
doi: 10.3836/tjm/1264170239. |
[11] |
O. A. Ladyzhenskaya, "The Mathematical Theory of Viscous Incompressible Flow," Second English edition, revised and enlarged,, Translated from the Russian by Richard A. Silverman and John Chu, (1969).
|
[12] |
J. Leray, Etude de diverses équations intégrales nonlinéaires et de quelques problèmes que pose l'hydrodynamique,, J. Math. Pure Appl., 12 (1933), 1. Google Scholar |
[13] |
J. L. Lions, "Quelques méthodes de résolution des problèmes aux limites non linéaires,", Dunod, (1969).
|
[14] |
H. Morimoto, On the existence of periodic weak solutions of the Navier-Stokes equations in regions with periodically moving boundaries,, J. Fac. Sci. Univ. Tokyo, 18 (): 499.
|
[15] |
H. Morimoto, Non-stationary Boussinesq equations,, J. Fac. Science Univ. Tokyo Sec. IA, 39 (1992), 61.
|
[16] |
H. Morimoto, General outflow condition for Navier-Stokes flow,, in, 16 (1998), 209.
|
[17] |
H. Morimoto, A remark on the existence of 2-D steady Navier-Stokes flow in symmetric domain under general outflow condition,, J. Math. Fluid Mech., 9 (2007), 411.
doi: 10.1007/s00021-005-0206-2. |
[18] |
H. Morimoto, Time periodic Navier-Stokes flow with nonhomogeneous boundary condition,, Journal of Mathematical Sciences The University of Tokyo, 16 (2009), 113.
|
[19] |
H. Morimoto, Heat convection equation with nonhomogeneous boundary condition,, Funkciaj Ekvacioj, 53 (2010), 213.
doi: 10.1619/fesi.53.213. |
[20] |
K. Ōeda, Weak and strong solutions of the heat convection equations in regions with moving boundaries,, J. Fac. Science, 36 (1989), 491.
|
[21] |
G. Prodi, Qualche risultato riguardo alle equazioni di Navier-Stokes nel caso di bidimensionale,, Rendi Semi. Mat. Univ. Padova, 30 (1960), 1.
|
[22] |
J. Serrin, A note on the existence of periodic solutions of the Navier-Stokes equations,, Arch. Rational Mech. Anal., 3 (1959), 120.
doi: 10.1007/BF00284169. |
[23] |
A. Takeshita, On the reproductive property of 2-dimensional Navier-Stokes equations,, J. Fac. Sci. Univ. Tokyo Sect. I, 16 (1970), 297.
|
[24] |
A. Takeshita, A remark on Leray's inequality,, Pacific J. Math., 157 (1993), 151.
|
[25] |
I. Yudovič, Periodic motions of a viscous incompressible fluid,, Doklady Acad. Nauk., 130 (1960), 1214.
|
show all references
References:
[1] |
C. J. Amick, Existence of solutions to the nonhomogeneous steady Navier-Stokes equations,, Indiana Univ. Math. J., 33 (1984), 817.
doi: 10.1512/iumj.1984.33.33043. |
[2] |
R. Farwig and H. Morimoto, Leray's inequality for fluid flow in symmetric multi-connected doamins,, Darmstadt University of Technology, 2612 (2010). Google Scholar |
[3] |
H. Fujita, On the existence and regularity of the steady-state solutions of the Navier-Stokes theorem,, J. Fac. Sci. Univ. Tokyo, 9 (1961), 59.
|
[4] |
H. Fujita, On stationary solutions to Navier-Stokes equations in symmetric plane domains under general outflow condition,, in, 388 (1998), 16.
|
[5] |
G. P. Galdi, "An Introduction to the Mathematical Theory of the Navier-Stokes Equations. Vol. II, Nonlinear Steady Problems,", Springer Tracts in Natural Philosophy, 39 (1994).
|
[6] |
E. Hopf, Ein allgemeiner Endlichkeitssatz der Hydrodynamik,, Math. Ann., 117 (1941), 764.
doi: 10.1007/BF01450040. |
[7] |
E. Hopf, "On Nonlinear Partial Differential Equations,", Lecture Series of the Symposium on Partial Differential Equations, (1957), 1. Google Scholar |
[8] |
H. Inoue and M. Ôtani, Periodic Problems for Heat Convection Equations in Noncylindrical Domains,, Funkcialaj Ekvacioj, 40 (1997), 19.
|
[9] |
S. Kaniel and M. Shinbrot, A reproductive property of the Navier-Stokes eqautions,, Arch. Rat. Mech. Anal., 24 (1967), 363.
doi: 10.1007/BF00253153. |
[10] |
T-P. Kobayashi, Time periodic solutions of the Navier-Stokes equations under general outflow condition,, Tokyo Journal of Mathematics, 32 (2009), 409.
doi: 10.3836/tjm/1264170239. |
[11] |
O. A. Ladyzhenskaya, "The Mathematical Theory of Viscous Incompressible Flow," Second English edition, revised and enlarged,, Translated from the Russian by Richard A. Silverman and John Chu, (1969).
|
[12] |
J. Leray, Etude de diverses équations intégrales nonlinéaires et de quelques problèmes que pose l'hydrodynamique,, J. Math. Pure Appl., 12 (1933), 1. Google Scholar |
[13] |
J. L. Lions, "Quelques méthodes de résolution des problèmes aux limites non linéaires,", Dunod, (1969).
|
[14] |
H. Morimoto, On the existence of periodic weak solutions of the Navier-Stokes equations in regions with periodically moving boundaries,, J. Fac. Sci. Univ. Tokyo, 18 (): 499.
|
[15] |
H. Morimoto, Non-stationary Boussinesq equations,, J. Fac. Science Univ. Tokyo Sec. IA, 39 (1992), 61.
|
[16] |
H. Morimoto, General outflow condition for Navier-Stokes flow,, in, 16 (1998), 209.
|
[17] |
H. Morimoto, A remark on the existence of 2-D steady Navier-Stokes flow in symmetric domain under general outflow condition,, J. Math. Fluid Mech., 9 (2007), 411.
doi: 10.1007/s00021-005-0206-2. |
[18] |
H. Morimoto, Time periodic Navier-Stokes flow with nonhomogeneous boundary condition,, Journal of Mathematical Sciences The University of Tokyo, 16 (2009), 113.
|
[19] |
H. Morimoto, Heat convection equation with nonhomogeneous boundary condition,, Funkciaj Ekvacioj, 53 (2010), 213.
doi: 10.1619/fesi.53.213. |
[20] |
K. Ōeda, Weak and strong solutions of the heat convection equations in regions with moving boundaries,, J. Fac. Science, 36 (1989), 491.
|
[21] |
G. Prodi, Qualche risultato riguardo alle equazioni di Navier-Stokes nel caso di bidimensionale,, Rendi Semi. Mat. Univ. Padova, 30 (1960), 1.
|
[22] |
J. Serrin, A note on the existence of periodic solutions of the Navier-Stokes equations,, Arch. Rational Mech. Anal., 3 (1959), 120.
doi: 10.1007/BF00284169. |
[23] |
A. Takeshita, On the reproductive property of 2-dimensional Navier-Stokes equations,, J. Fac. Sci. Univ. Tokyo Sect. I, 16 (1970), 297.
|
[24] |
A. Takeshita, A remark on Leray's inequality,, Pacific J. Math., 157 (1993), 151.
|
[25] |
I. Yudovič, Periodic motions of a viscous incompressible fluid,, Doklady Acad. Nauk., 130 (1960), 1214.
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