An approximation theorem of Wong-Zakai type for stochastic Navier-Stokes equations
Rendiconti del Seminario Matematico della Università di Padova (1996)
- Volume: 96, page 15-36
- ISSN: 0041-8994
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topTwardowska, Krystyna. "An approximation theorem of Wong-Zakai type for stochastic Navier-Stokes equations." Rendiconti del Seminario Matematico della Università di Padova 96 (1996): 15-36. <http://eudml.org/doc/108407>.
@article{Twardowska1996,
author = {Twardowska, Krystyna},
journal = {Rendiconti del Seminario Matematico della Università di Padova},
keywords = {Wong-Zakai approximation theorem; stochastic Navier-Stokes equations; Wiener process; Itô correction term},
language = {eng},
pages = {15-36},
publisher = {Seminario Matematico of the University of Padua},
title = {An approximation theorem of Wong-Zakai type for stochastic Navier-Stokes equations},
url = {http://eudml.org/doc/108407},
volume = {96},
year = {1996},
}
TY - JOUR
AU - Twardowska, Krystyna
TI - An approximation theorem of Wong-Zakai type for stochastic Navier-Stokes equations
JO - Rendiconti del Seminario Matematico della Università di Padova
PY - 1996
PB - Seminario Matematico of the University of Padua
VL - 96
SP - 15
EP - 36
LA - eng
KW - Wong-Zakai approximation theorem; stochastic Navier-Stokes equations; Wiener process; Itô correction term
UR - http://eudml.org/doc/108407
ER -
References
top- [1] P. Aquistapace - B. Terreni, An approach to Itô linear equations in Hilbert spaces by approximation of white noise with coloured noise, Stochastic Anal. Appl., 2 (1984), pp. 131-186. Zbl0547.60066MR746434
- [2] A. Bensoussan, A model of stochastic differential equation in Hilbert space applicable to Navier-Stokes equation in dimension 2, in: Stochastic Analysis, Liber Amicorum for Moshe Zakai, E ds. E. Mayer-Wolf, E. Merzbach and A. Schwartz, Academic Press (1991), pp. 51-73. Zbl0731.60054MR1119823
- [3] A. Bensoussan - R. TEMAM, Equations stochastiques du type Navier-Stokes, J. Functional Analysis, 13 (1973), pp. 195-222. Zbl0265.60094MR348841
- [4] Z. Brze - M. Capi - F. Flandoli, Stochastic Navier-Stokes equations with multiplicative noise, Stochastic Anal. Appl., 10, 5 (1992), pp. 523-532. Zbl0762.35083MR1185046
- [5] Z. Brze - M. Capi - F. Flandoli, A convergence result for stochastic partial differential equations, Stochastics, 24 (1988), pp. 423-445. Zbl0653.60049MR972973
- [6] M. Capiński, A note on uniqueness of stochastic Navier-Stokes equations, Universitatis Iagellonicae Acta Math., 30 (1993), pp. 219-228. Zbl0858.60057MR1233785
- [7] M. Capi - N. Cutland, Stochastic Navier-Stokes equations, Acta Applicandae Math., 25 (1991), pp. 59-85. Zbl0746.60065MR1140758
- [8] R.F. Curtain - A.J. Pritchard, Infinite Dimensional Linear System Theory, Springer, Berlin (1978). Zbl0389.93001MR516812
- [9] H. Doss, Liens entre équations différentielles stochastiques et ordinaires, Ann. Inst. H. Poincaré, 13, 2 (1977), pp. 99-125. Zbl0359.60087MR451404
- [10] H. Fujita-Yashima, Equations de Navier-Stokes stochastiques non homogénes et applications, Scuola Normale Superiore, Pisa (1992). Zbl0753.35066
- [11] I. Gyöngy, On stochastic equations with respect to semimartingales III, Stochastics, 7 (1982), pp. 231-254. Zbl0495.60067MR674448
- [12] I. Gyöngy, The stability of stochastic partial differential equations and applications. Theorems on supports, Lecture Notes in Math., 1390, Springer, Berlin (1989), pp. 91-118. Zbl0683.93092MR1019596
- [13] N. Ikeda - S. WATANABE, Stochastic Differential Equations and Diffusion Processes, North-Holland, Amsterdam (1981). Zbl0684.60040MR1011252
- [14] N.U. Krylov - B.L. Rozovskii, On stochastic evolution equations, Itogi Nauki i Techniki, Teor. Verojatn. Moscow, 14 (1979). pp. 71-146 (in Russian). Zbl0436.60047MR570795
- [15] J.L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod, Paris (1969). Zbl0189.40603MR259693
- [16] J.L. Lions - E. MAGENES, Non-Homogeneous Boundary Value Problems and Applications, Springer, Berlin (1972). Zbl0223.35039
- [17] W. Mackevi, On the support of a solution of stochastic differential equation, Lietuvos Matematikos Rinkinys, 26, 1 (1986), pp. 91-98. Zbl0621.60062MR847207
- [18] S. Nakao - Y. Yamato, Approximation theorem of stochastic differential equations, Proc. Internat. Sympos. SDE Kyoto1976, Tokyo (1978), pp. 283-296. Zbl0443.60051MR536015
- [19] E. Pardoux, Equations aux dérivées partielles stochastiques non linéaires monotones. Etude de solutions fortes de type Itô, Thèse Doct. Sci. Math. Univ. Paris Sud (1975).
- [20] B. Schmalfuss, Measure attractors of the stochastic Navier-Stokes equations, University Bremen, Report Nr. 258, Bremen (1991). MR1121219
- [21] R. Temam, Infinite Dimensional Dynamical Systems in Mechanics and Physics, Springer, Berlin (1988). Zbl0662.35001MR953967
- [22] R. Temam, Navier-Stokes Equations, North-Holland, Amsterdam (1977). Zbl0383.35057MR603444
- [23] K. Twardowska, An approximation theorem of Wong-Zakai type for nonlinear stochastic partial differential equations, Stochastic Anal. Appl., 13, 5 (1995), pp. 601-626. Zbl0839.60059MR1353194
- [24] K. Twardowska, An extension of the Wong-Zakai theorem for stochastic evolution equations in Hilbert spaces, Stochastic Anal. Appl., 10, 4 (1992), pp. 471-500. Zbl0754.60060MR1178488
- [25] K. Twardowska, Approximation theorems of Wong-Zakai type for stochastic differential equations in infinite dimensions, Dissertationes Math., 325 (1993), pp. 1-54. Zbl0777.60051MR1215779
- [26] M.J. Vishik - A.V. Fursikov, Mathematical Problems of Statistical Hydromechanics, Kluwer, Dordrecht (1988). Zbl0688.35077
- [27] E Wong - M. Zakai, On the convergence of ordinary integrals to stochastic integrals, Ann. Math. Statist., 36 (1965), pp. 1560-1564. Zbl0138.11201MR195142
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