Diffusion-Approximations for Navier-Stokes Equation in Space-Time Gaussian Velocity Field

References

• Adler , R.J. 1981 . The Geometry of Random Fields New York , , Singapore : John Wiley & Sons Ltd. .
   Google Scholar
• Brezeźniak , Z. , Capiński , M. and Flandoli , F. 1991 . Stochastic partial differential equations and turbulence . Math. Models Methods Appl. Sci. , 1 : 41 – 59 .
   Google Scholar
• Carmona , R.A. and Fouque , J.P. 1995 . “ Diffusion-approximation for the advection–diffusion of a passive scalar by a space-time Gaussian velocity field ” . In Seminar on Stochastic Analysis, Random Fields and Applications Edited by: Bolthausen , E. , Dozzi , M. and Russo , F. 37 – 52 . Bersel , , Singapore : Birkhäuser Verlag .
   Google Scholar
• Clouet , J.F. 1996 . A diffusion-approximation theorem in Navier-Stokes equation . Stoch. Anal. Appl. , 14 : 33 – 46 .
   Web of Science ®Google Scholar
• Galdi , G.P. 2000 . “ An introduction to the Navier-Stokes initial-boundary value problem ” . In Fundamental Directions in Mathematical Fluid Mechanics Edited by: Galdi , G.P. , Heywood , J.G. and Rannacher , R. 1 – 70 . Basel , , Singapore : Birkhäuser Verlag .
   Google Scholar
• Kallianpur , G. and Xiong , J. 1995 . Stochastic Differential Equations in Infinite Dimentional Spaces Hayward , CA : Institute of Mathematical Statistics .
   Google Scholar
• Kushner , H. and Huang , H. 1985 . Limits for parabolic partial differential equations with wide band stochastic coefficient and an application to filtering theory . Stochastics , 14 : 115 – 148 .
   Google Scholar
• Masuda , K. 1984 . Weak solutions of Navier-Stokes equations . Toˆhoku Math. J. , 36 : 623 – 646 .
   Web of Science ®Google Scholar
• Mikulevicius , R. and Rozovskii , B. 2001 . “ On equations of stochastic fluid mechanics ” . In Stochastics in Finite and Infinite Dimensions Edited by: Hida , T. 285 – 302 . Boston , , Singapore : Birkhäuser Verlag .
   Google Scholar
• Mitoma , I. 1983 . Tightness of probabilities on C([0, 1];𝒮') and D([0, 1];𝒮') . Ann. Probab. , 11 : 989 – 999 .
   Web of Science ®Google Scholar
• Komorowski , T. 1996 . Diffusion approximation for the advection of particles in a strongly turbulent random environment . Ann. Probab. , 24 : 346 – 376 . [CROSSREF]
   Web of Science ®Google Scholar
• Temam , R. 1979 . Navier-Stokes Equations Amsterdam , , Singapore : North-Holland Publishing Company .
   Google Scholar
• Watanabe , H. 1989 . On the convergence of partial differential equations of parabolic type with rapidly oscillating coefficients to stochastic partial differential equations . Appl. Math. Optim. , 20 : 81 – 96 .
   Web of Science ®Google Scholar