Measure Attractors for Stochastic Navier-Stokes Equations

Marek Capinski (Jagiellonian University)
Nigel J. Cutland (University of Hull)

Abstract


We show existence of measure attractors for 2-D stochastic Navier-Stokes equations with general multiplicative noise.

Full Text: Download PDF | View PDF online (requires PDF plugin)

Pages: 1-15

Publication Date: May 20, 1998

DOI: 10.1214/EJP.v3-30

References

  1. S.Albeverio, J.-E.Fenstad, R.Hoegh-Krohn, and T.Lindstrøm, Nonstandard Methods in Stochastic Analysis and Mathematical Physics, Academic Press, New York 1986. Math Review 88f:03061
  2. A.Bensoussan, R.Temam, Equations stochastiques du type Navier-Stokes, J. Functional Anal. 13(1973), 195-222. Math Review 50:1336
  3. M.Capinski, N.J.Cutland, Stochastic Navier-Stokes equations, Acta Applicandae Mathematicae 25 (1991), 59-85. Math Review 93b:35108
  4. M.Capinski, N.J.Cutland, Nonstandard Methods for Stochastic Fluid Mechanics, World Scientific, Singapore 1995. Math Review 96g:35222
  5. M.Capinski, D.Gatarek, Stochastic equations in Hilbert space with application to Navier-Stokes equations in any dimension, Journal of Functional Analysis 126 (1994), 26-35. Math Review 95j:60094
  6. H.Crauel and F.Flandoli, Attractors for random dynamical systems, Probab. Theory Related Fields 100(1994), 365-393. Math Review 95k:58092
  7. G.Da Prato and J.Zabczyk, Stochastic Equations in Infinite Dimension, Cambridge University Press, Cambridge 1992. Math Review 95g:60073
  8. C.Foias, Statistical study of Navier-Stokes equations I, Rend. Sem. Mat. Univ. Padova 48 (1973), 219-348. Math Review 50:5220
  9. O.A.Ladyzhenskaya, A dynamical system generated by the Navier-Stokes equations, J. Soviet Math. 3(1975), 458-479 Math Review 48:6720
  10. H.Morimoto, Attractors of probability measures for semilinear stochastic evolution equations, Stoch. Anal. Appl. 2:10(1992), 205-212. Math Review 93e:60113
  11. B.Schmalfuss , Long-time behaviour of the stochastic Navier-Stokes equations, Math. Nach. 152 (1991), 7-20. Math Review 92e:35179
  12. B.Schmalfuss , Measure attractors of the stochastic Navier-Stokes equation, Bremen Report no.258, 1991. Math Review number not available.
  13. B.Schmalfuss , Measure attractors and stochastic attractors, Bremen Report no. 332, 1995. Math Review number not available.
  14. R.Temam, Navier-Stokes Equations, Theory and Numerical Analysis, 3rd rev edition, North-Holland, Amsterdam, 1984. Math Review 58:29439
  15. R.Temam, Infinite-Dimensional Dynamical Systems in Mechanics and Physics, Springer-Verlag, New York 1988; 2nd edition 1997. Math Review 98b:58056
  16. V.S.Varadarajan, Measures on topological spaces, American Math. Soc Translations, Series 2, 48 (1961), 161-228. Math Review 26:6342
Bookmark and Share


Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.