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The existence and decay estimates of the solutions to $3$D stochastic Navier-Stokes equations with additive noise in an exterior domain
1. | Division of Mathematical Sciences, Graduate School of Comparative Culture, Kurume University, Miimachi, Kurume, Fukuoka 839-8502, Japan |
References:
[1] |
M. Capinski and D. Gatarek, Stochastic equations in Hilbert space with application to Navier-Stokes equations in any dimension, J. Functional Analysis, 126 (1994), 26-35.
doi: 10.1006/jfan.1994.1140. |
[2] |
T. Caraballo, J. Langa and T. Taniguchi, The exponential behavior and stabilizability of stochastic 2D-Navier-Stokes equations, J. Diff. Equations, 179 (2002), 714-737.
doi: 10.1006/jdeq.2001.4037. |
[3] |
G. Da Prato and J. Zabczyk, Stochastic Equations in Infinite Dimensions, Cambridge University Press, 1992.
doi: 10.1017/CBO9780511666223. |
[4] |
G. Da Prato and J. Zabczyk, Ergodicity for Infinite Dimensional Systems, Cambridge University Press, 1996.
doi: 10.1017/CBO9780511662829. |
[5] |
F. Flandoli and D. Gatarek, Martingale and stationary solutions for stochastic Naver-Stokes equations, Proba. Theory and Related Fields, 102 (1995), 367-391.
doi: 10.1007/BF01192467. |
[6] |
H. Fujita and T. Kato, On the Navier-Stokes initial value problem. I, Arch. Rational Mech. Anal., 16 (1964), 269-315.
doi: 10.1007/BF00276188. |
[7] |
Y. Giga and T. Miyakawa, Solution in $L_r$ of the Navier-Stokes initial value problem, Arch. Rational Mech. Anal., 89 (1985), 267-281.
doi: 10.1007/BF00276875. |
[8] |
T. Kato and H. Fujita, On the nonstationary Navier-Stokes system, Rend. Semi. Math. Univ. Padova, 32 (1962), 243-260. |
[9] |
T. Kato, Strong $L^p-$solutions of the Navier-Stokes equation in $R^n$, with applications to weak solutions, Math. Z., 187 (1984), 471-480.
doi: 10.1007/BF01174182. |
[10] |
T. Miyakawa, On nonstationary solution of the Navier-Stokes equations in an exterior domain, Hiroshima Math. J., 12 (1982), 115-140. |
[11] |
A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer, 1983.
doi: 10.1007/978-1-4612-5561-1. |
[12] |
J. Seidler and T. Sobukawa, Exponential integrability of stochastic convolutions, J. London Math. Soc., 67 (2003), 245-258.
doi: 10.1112/S0024610702003745. |
[13] |
H. Sohr, The Navier-Stokes Equations: An Elementary Functional Analysis Approach, Birkhäuser, Boston, 2001.
doi: 10.1007/978-3-0348-8255-2. |
[14] |
S. Sritharan and P. Sundar, Large deviations for the two-dimensional Navier-Stokes equations with multiplicative noise, Stochastic Processes and Applications, 116 (2006), 1636-1659.
doi: 10.1016/j.spa.2006.04.001. |
[15] |
T. Taniguchi, The exponential behaviour of Navier-Stokes equations with time delay external force, Discrete Continuous Dynamical Systems-A, 12 (2005), 997-1018.
doi: 10.3934/dcds.2005.12.997. |
[16] |
T. Taniguchi, Asymptotic stability theorems of semilinear stochastic evolution equations in Hilbert spaces, Stochastics and Stochastics Reports, 53 (1994), 41-52.
doi: 10.1080/17442509508833982. |
[17] |
T. Taniguchi, The existence of energy solutions to 2-dimensional non-Lipschitz stochastic Navier-Stokes equations in unbounded domains, J. Diff. Equations, 251 (2011), 3329-3362.
doi: 10.1016/j.jde.2011.07.029. |
[18] |
R. Temam, Infinite Dimensional Dynamical Systems in Mechanics and Physics, 2nd edition, Springer, New York.
doi: 10.1007/978-1-4684-0313-8. |
[19] |
M. Wiegner, Decay estimates for strong solutions of the Navier-Stokes equations in exterior domain, Ann. Univ. Ferrara-Sez. VII (N.S.), 46 (2000), 61-79. |
show all references
References:
[1] |
M. Capinski and D. Gatarek, Stochastic equations in Hilbert space with application to Navier-Stokes equations in any dimension, J. Functional Analysis, 126 (1994), 26-35.
doi: 10.1006/jfan.1994.1140. |
[2] |
T. Caraballo, J. Langa and T. Taniguchi, The exponential behavior and stabilizability of stochastic 2D-Navier-Stokes equations, J. Diff. Equations, 179 (2002), 714-737.
doi: 10.1006/jdeq.2001.4037. |
[3] |
G. Da Prato and J. Zabczyk, Stochastic Equations in Infinite Dimensions, Cambridge University Press, 1992.
doi: 10.1017/CBO9780511666223. |
[4] |
G. Da Prato and J. Zabczyk, Ergodicity for Infinite Dimensional Systems, Cambridge University Press, 1996.
doi: 10.1017/CBO9780511662829. |
[5] |
F. Flandoli and D. Gatarek, Martingale and stationary solutions for stochastic Naver-Stokes equations, Proba. Theory and Related Fields, 102 (1995), 367-391.
doi: 10.1007/BF01192467. |
[6] |
H. Fujita and T. Kato, On the Navier-Stokes initial value problem. I, Arch. Rational Mech. Anal., 16 (1964), 269-315.
doi: 10.1007/BF00276188. |
[7] |
Y. Giga and T. Miyakawa, Solution in $L_r$ of the Navier-Stokes initial value problem, Arch. Rational Mech. Anal., 89 (1985), 267-281.
doi: 10.1007/BF00276875. |
[8] |
T. Kato and H. Fujita, On the nonstationary Navier-Stokes system, Rend. Semi. Math. Univ. Padova, 32 (1962), 243-260. |
[9] |
T. Kato, Strong $L^p-$solutions of the Navier-Stokes equation in $R^n$, with applications to weak solutions, Math. Z., 187 (1984), 471-480.
doi: 10.1007/BF01174182. |
[10] |
T. Miyakawa, On nonstationary solution of the Navier-Stokes equations in an exterior domain, Hiroshima Math. J., 12 (1982), 115-140. |
[11] |
A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer, 1983.
doi: 10.1007/978-1-4612-5561-1. |
[12] |
J. Seidler and T. Sobukawa, Exponential integrability of stochastic convolutions, J. London Math. Soc., 67 (2003), 245-258.
doi: 10.1112/S0024610702003745. |
[13] |
H. Sohr, The Navier-Stokes Equations: An Elementary Functional Analysis Approach, Birkhäuser, Boston, 2001.
doi: 10.1007/978-3-0348-8255-2. |
[14] |
S. Sritharan and P. Sundar, Large deviations for the two-dimensional Navier-Stokes equations with multiplicative noise, Stochastic Processes and Applications, 116 (2006), 1636-1659.
doi: 10.1016/j.spa.2006.04.001. |
[15] |
T. Taniguchi, The exponential behaviour of Navier-Stokes equations with time delay external force, Discrete Continuous Dynamical Systems-A, 12 (2005), 997-1018.
doi: 10.3934/dcds.2005.12.997. |
[16] |
T. Taniguchi, Asymptotic stability theorems of semilinear stochastic evolution equations in Hilbert spaces, Stochastics and Stochastics Reports, 53 (1994), 41-52.
doi: 10.1080/17442509508833982. |
[17] |
T. Taniguchi, The existence of energy solutions to 2-dimensional non-Lipschitz stochastic Navier-Stokes equations in unbounded domains, J. Diff. Equations, 251 (2011), 3329-3362.
doi: 10.1016/j.jde.2011.07.029. |
[18] |
R. Temam, Infinite Dimensional Dynamical Systems in Mechanics and Physics, 2nd edition, Springer, New York.
doi: 10.1007/978-1-4684-0313-8. |
[19] |
M. Wiegner, Decay estimates for strong solutions of the Navier-Stokes equations in exterior domain, Ann. Univ. Ferrara-Sez. VII (N.S.), 46 (2000), 61-79. |
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