Rough flows and homogenization in stochastic turbulence

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Bailleul, I.; Catellier, R.;
  • Subject: Mathematical Physics | Mathematics - Probability | Mathematics - Dynamical Systems

We provide in this work a tool-kit for the study of homogenisation of random ordinary differential equations, under the form of a friendly-user black box based on the tehcnology of rough flows. We illustrate the use of this setting on the example of stochastic turbulenc... View more
  • References (20)
    20 references, page 1 of 2

    [1] Pavliotis, G. and Stuart, A., Multiscale methods, averaging and homogenization. Springer, 2008.

    [2] Kabanov, Y., Two-scale stochastic systems. Springer, 2003.

    [3] CIoranescu, D. and Donato, P., An introduction to homogenization. Oxford Lecture Series in Math. 17, 1999.

    [4] Tartar, L., The general theory of homogenization, a personalized introduction. Lect. Notes Unione Mat. Italiana 7, Springer, 2009.

    [5] Otto, F. and Gloria, A., The corrector in stochastic homogenization: Near-optimal rates with optimal stochastic integrability. arXiv:1510.08290, 2015.

    [6] Armstrong, S. and Kuusi, T. and Mourrat, J.-C., Mesoscopic higher regularity and subadditivity in elliptic homogenization. arXiv:1507.06935, 2015.

    [7] Armstrong, S. and Gloria, A. and Kuusi, T., Bounded correctors in almost periodic homogenization. arXiv:1509.08390, 2015.

    [8] Kesten, H. and Papanicolaou, G., A limit theorem for turbulent diffusion. Comm. Math. Phys. 65:97-128, 1979.

    [9] Kesten, H. and Papanicolaou, G., A limit theorem for stochastic acceleration. Comm. Math. Phys. 78:19-63, 1980.

    [10] Papanicolaou, G. and Stroock, D. and Varadhan, S., Martingale approach to some limit theorems Papers from the Duke Turbulence Conference (Duke Univ., Durham, N.C., 1976), Paper No. 6, ii+120 pp. Duke Univ. Math. Ser., Vol. III, Duke Univ., Durham, N.C., 1977.

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