An approximation theorem of Wong-Zakai type for stochastic Navier-Stokes equations

Krystyna Twardowska

Rendiconti del Seminario Matematico della Università di Padova (1996)

  • Volume: 96, page 15-36
  • ISSN: 0041-8994

How to cite

top

Twardowska, 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. [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. [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. [3] A. Bensoussan - R. TEMAM, Equations stochastiques du type Navier-Stokes, J. Functional Analysis, 13 (1973), pp. 195-222. Zbl0265.60094MR348841
  4. [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. [5] Z. Brze - M. Capi - F. Flandoli, A convergence result for stochastic partial differential equations, Stochastics, 24 (1988), pp. 423-445. Zbl0653.60049MR972973
  6. [6] M. Capiński, A note on uniqueness of stochastic Navier-Stokes equations, Universitatis Iagellonicae Acta Math., 30 (1993), pp. 219-228. Zbl0858.60057MR1233785
  7. [7] M. Capi - N. Cutland, Stochastic Navier-Stokes equations, Acta Applicandae Math., 25 (1991), pp. 59-85. Zbl0746.60065MR1140758
  8. [8] R.F. Curtain - A.J. Pritchard, Infinite Dimensional Linear System Theory, Springer, Berlin (1978). Zbl0389.93001MR516812
  9. [9] H. Doss, Liens entre équations différentielles stochastiques et ordinaires, Ann. Inst. H. Poincaré, 13, 2 (1977), pp. 99-125. Zbl0359.60087MR451404
  10. [10] H. Fujita-Yashima, Equations de Navier-Stokes stochastiques non homogénes et applications, Scuola Normale Superiore, Pisa (1992). Zbl0753.35066
  11. [11] I. Gyöngy, On stochastic equations with respect to semimartingales III, Stochastics, 7 (1982), pp. 231-254. Zbl0495.60067MR674448
  12. [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. [13] N. Ikeda - S. WATANABE, Stochastic Differential Equations and Diffusion Processes, North-Holland, Amsterdam (1981). Zbl0684.60040MR1011252
  14. [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. [15] J.L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod, Paris (1969). Zbl0189.40603MR259693
  16. [16] J.L. Lions - E. MAGENES, Non-Homogeneous Boundary Value Problems and Applications, Springer, Berlin (1972). Zbl0223.35039
  17. [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. [18] S. Nakao - Y. Yamato, Approximation theorem of stochastic differential equations, Proc. Internat. Sympos. SDE Kyoto1976, Tokyo (1978), pp. 283-296. Zbl0443.60051MR536015
  19. [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. [20] B. Schmalfuss, Measure attractors of the stochastic Navier-Stokes equations, University Bremen, Report Nr. 258, Bremen (1991). MR1121219
  21. [21] R. Temam, Infinite Dimensional Dynamical Systems in Mechanics and Physics, Springer, Berlin (1988). Zbl0662.35001MR953967
  22. [22] R. Temam, Navier-Stokes Equations, North-Holland, Amsterdam (1977). Zbl0383.35057MR603444
  23. [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. [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. [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. [26] M.J. Vishik - A.V. Fursikov, Mathematical Problems of Statistical Hydromechanics, Kluwer, Dordrecht (1988). Zbl0688.35077
  27. [27] E Wong - M. Zakai, On the convergence of ordinary integrals to stochastic integrals, Ann. Math. Statist., 36 (1965), pp. 1560-1564. Zbl0138.11201MR195142

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.