An approximation theorem of Wong-Zakai type for stochastic Navier-Stokes equations
Rendiconti del Seminario Matematico della Università di Padova, Tome 96 (1996), pp. 15-36.
@article{RSMUP_1996__96__15_0,
     author = {Twardowska, Krystyna},
     title = {An approximation theorem of {Wong-Zakai} type for stochastic {Navier-Stokes} equations},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     pages = {15--36},
     publisher = {Seminario Matematico of the University of Padua},
     volume = {96},
     year = {1996},
     mrnumber = {1438286},
     zbl = {0882.35140},
     language = {en},
     url = {http://www.numdam.org/item/RSMUP_1996__96__15_0/}
}
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Twardowska, Krystyna. An approximation theorem of Wong-Zakai type for stochastic Navier-Stokes equations. Rendiconti del Seminario Matematico della Università di Padova, Tome 96 (1996), pp. 15-36. http://www.numdam.org/item/RSMUP_1996__96__15_0/

[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. | MR | Zbl

[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. | MR | Zbl

[3] A. Bensoussan - R. TEMAM, Equations stochastiques du type Navier-Stokes, J. Functional Analysis, 13 (1973), pp. 195-222. | MR | Zbl

[4] Z. Brze - M. Capi - F. Flandoli, Stochastic Navier-Stokes equations with multiplicative noise, Stochastic Anal. Appl., 10, 5 (1992), pp. 523-532. | MR | Zbl

[5] Z. Brze - M. Capi - F. Flandoli, A convergence result for stochastic partial differential equations, Stochastics, 24 (1988), pp. 423-445. | MR | Zbl

[6] M. Capiński, A note on uniqueness of stochastic Navier-Stokes equations, Universitatis Iagellonicae Acta Math., 30 (1993), pp. 219-228. | MR | Zbl

[7] M. Capi - N. Cutland, Stochastic Navier-Stokes equations, Acta Applicandae Math., 25 (1991), pp. 59-85. | MR | Zbl

[8] R.F. Curtain - A.J. Pritchard, Infinite Dimensional Linear System Theory, Springer, Berlin (1978). | MR | Zbl

[9] H. Doss, Liens entre équations différentielles stochastiques et ordinaires, Ann. Inst. H. Poincaré, 13, 2 (1977), pp. 99-125. | EuDML | Numdam | MR | Zbl

[10] H. Fujita-Yashima, Equations de Navier-Stokes stochastiques non homogénes et applications, Scuola Normale Superiore, Pisa (1992). | Zbl

[11] I. Gyöngy, On stochastic equations with respect to semimartingales III, Stochastics, 7 (1982), pp. 231-254. | MR | Zbl

[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. | MR | Zbl

[13] N. Ikeda - S. WATANABE, Stochastic Differential Equations and Diffusion Processes, North-Holland, Amsterdam (1981). | MR | Zbl

[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). | MR | Zbl

[15] J.L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod, Paris (1969). | MR

[16] J.L. Lions - E. MAGENES, Non-Homogeneous Boundary Value Problems and Applications, Springer, Berlin (1972). | Zbl

[17] W. Mackevi, On the support of a solution of stochastic differential equation, Lietuvos Matematikos Rinkinys, 26, 1 (1986), pp. 91-98. | MR | Zbl

[18] S. Nakao - Y. Yamato, Approximation theorem of stochastic differential equations, Proc. Internat. Sympos. SDE Kyoto 1976, Tokyo (1978), pp. 283-296. | MR | Zbl

[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). | MR

[21] R. Temam, Infinite Dimensional Dynamical Systems in Mechanics and Physics, Springer, Berlin (1988). | MR | Zbl

[22] R. Temam, Navier-Stokes Equations, North-Holland, Amsterdam (1977). | MR | Zbl

[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. | MR | Zbl

[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. | MR | Zbl

[25] K. Twardowska, Approximation theorems of Wong-Zakai type for stochastic differential equations in infinite dimensions, Dissertationes Math., 325 (1993), pp. 1-54. | MR | Zbl

[26] M.J. Vishik - A.V. Fursikov, Mathematical Problems of Statistical Hydromechanics, Kluwer, Dordrecht (1988).

[27] E Wong - M. Zakai, On the convergence of ordinary integrals to stochastic integrals, Ann. Math. Statist., 36 (1965), pp. 1560-1564. | MR | Zbl