Ergodicity, mixing and KAM
Kuksin, Sergei1, 2, 3
1 Institut de Mathématiques de Jussieu-Paris Rive Gauche, CNRS, Université Paris Diderot, UMR 7586, Sorbonne Paris Cité F-75013, Paris France
2 School of Mathematics Shandong University Jinan, 250100 PRC
3 Saint Petersburg State University Universitetskaya nab. St. Petersburg Russia
Séminaire Laurent Schwartz — EDP et applications (2018-2019), Exposé no. 8, 9 p.

In this note we review recent progress in the problem of mixing for a nonlinear PDE of parabolic type, perturbed by a bounded random force.

Publié le :
DOI : 10.5802/slsedp.128

Kuksin, Sergei 1, 2, 3

1 Institut de Mathématiques de Jussieu-Paris Rive Gauche, CNRS, Université Paris Diderot, UMR 7586, Sorbonne Paris Cité F-75013, Paris France
2 School of Mathematics Shandong University Jinan, 250100 PRC
3 Saint Petersburg State University Universitetskaya nab. St. Petersburg Russia 
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     author = {Kuksin, Sergei},
     title = {Ergodicity, mixing and {KAM}},
     journal = {S\'eminaire Laurent Schwartz {\textemdash} EDP et applications},
     note = {talk:8},
     pages = {1--9},
     year = {2018-2019},
     publisher = {Institut des hautes \'etudes scientifiques & Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
     doi = {10.5802/slsedp.128},
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     url = {https://www.numdam.org/articles/10.5802/slsedp.128/}
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Kuksin, Sergei. Ergodicity, mixing and KAM. Séminaire Laurent Schwartz — EDP et applications (2018-2019), Exposé no. 8, 9 p.. doi: 10.5802/slsedp.128

[1] M. Hairer and J. C. Mattingly, Ergodicity of the 2D Navier–Stokes equations with degenerate stochastic forcing, Ann. of Math. (2) 164 (2006), 993–1032. | MR | Zbl | DOI

[2] S. Kuksin, V. Nersesyan, A. Shirikyan, Exponential mixing for a class of dissipative PDEs with bounded degenerate noise, , 2018. | arXiv | MR | DOI

[3] S. Kuksin, H. Zang, Exponential mixing for dissipative PDEs with bounded non-degenerate noise, , 2018. | arXiv | DOI

[4] S. Kuksin, A. Shirikyan, Mathematics of Two-Dimensional Turbulence, CUP 2012. | Zbl | DOI

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