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Uspekhi Mat. Nauk, 2002, Volume 57, Issue 4(346), Pages 151–166 (Mi umn536)  

This article is cited in 11 scientific papers (total in 11 papers)

Analyticity of solutions for randomly forced two-dimensional Navier–Stokes equations

A. R. Shirikyan

Heriot Watt University

Abstract: A study is made of randomly forced two-dimensional Navier–Stokes equations with periodic boundary conditions. Under the assumption that the random forcing is analytic in the spatial variables and is a white noise in the time, it is proved that a large class of solutions, which contains all stationary solutions with finite energy, admits analytic continuation to a small complex neighbourhood of the torus. Moreover, a lower bound is obtained for the radius of analyticity in terms of the viscosity $\nu$, and it is shown that the Kolmogorov dissipation scale can be asymptotically estimated below by $\nu^{2+\delta}$ for any $\delta>0$.

DOI: https://doi.org/10.4213/rm536

Full text: PDF file (313 kB)
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English version:
Russian Mathematical Surveys, 2002, 57:4, 785–799

Bibliographic databases:

UDC: 517.95
MSC: Primary 35Q30, 35R60; Secondary 60H15, 35B65, 76D05
Received: 05.04.2002

Citation: A. R. Shirikyan, “Analyticity of solutions for randomly forced two-dimensional Navier–Stokes equations”, Uspekhi Mat. Nauk, 57:4(346) (2002), 151–166; Russian Math. Surveys, 57:4 (2002), 785–799

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Kuksin S., Shirikyan A., “Some limiting properties of randomly forced two-dimensional Navier–Stokes equations”, Proc. Roy. Soc. Edinburgh Sect. A, 133:4 (2003), 875–891  crossref  mathscinet  zmath  isi  elib
    2. Kuksin S., Shirikyan A., “Randomly forced CGL equation: stationary measures and the inviscid limit”, J. Phys. A, 37:12 (2004), 3805–3822  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    3. Lord G.J., Rougemont J., “A numerical scheme for stochastic PDEs with Gevrey regularity”, IMA J. Numer. Anal., 24:4 (2004), 587–604  crossref  mathscinet  zmath  isi  scopus  scopus
    4. Kuksin S.B., “The Eulerian limit for 2D statistical hydrodynamics”, J. Statist. Phys., 115:1-2 (2004), 469–492  crossref  mathscinet  zmath  adsnasa  isi  elib
    5. Shirikyan A., “Ergodicity for a class of Markov processes and applications to randomly forced PDE's. I”, Russ. J. Math. Phys., 12:1 (2005), 81–96  mathscinet  zmath  isi  elib
    6. Shirikyan A., “Law of large numbers and central limit theorem for randomly forced PDE's”, Probab. Theory Related Fields, 134:2 (2006), 215–247  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    7. Odasso C., “Spatial smoothness of the stationary solutions of the 3D Navier–Stokes equations”, Electron. J. Probab., 11 (2006), 686–699  crossref  mathscinet  zmath  isi  scopus  scopus
    8. Odasso C., “Exponential mixing for the 3D stochastic Navier–Stokes equations”, Comm. Math. Phys., 270:1 (2007), 109–139  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    9. Matthias Morzfeld, Xuemin Tu, Ethan Atkins, Alexandre J. Chorin, “A random map implementation of implicit filters”, Journal of Computational Physics, 2011  crossref  mathscinet  isi  scopus  scopus
    10. Hieber M., Stannat W., “Stochastic Stability of the Ekman Spiral”, Ann. Scuola Norm. Super. Pisa-Cl. Sci., 12:1 (2013), 189–208  mathscinet  zmath  isi
    11. Shao J., Guo B., Duan L., “Analytical Study of the Two-Dimensional Time-Fractional Navier-Stokes Equations”, J. Appl. Anal. Comput., 9:5 (2019), 1999–2022  crossref  isi
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