On recent progress for the stochastic Navier Stokes equations

Mattingly, Jonathan

doi:10.5802/jedp.625

Mattingly, Jonathan

Journées équations aux dérivées partielles (2003), article no. 11, 52 p.

Résumé

We give an overview of the ideas central to some recent developments in the ergodic theory of the stochastically forced Navier Stokes equations and other dissipative stochastic partial differential equations. Since our desire is to make the core ideas clear, we will mostly work with a specific example : the stochastically forced Navier Stokes equations. To further clarify ideas, we will also examine in detail a toy problem. A few general theorems are given. Spatial regularity, ergodicity, exponential mixing, coupling for a SPDE, and hypoellipticity are all discussed.

MR Zbl | 1 citation dans Numdam

DOI : 10.5802/jedp.625

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     pages = {1--52},
     publisher = {Universit\'e de Nantes},
     year = {2003},
     doi = {10.5802/jedp.625},
     mrnumber = {2050597},
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     language = {en},
     url = {http://www.numdam.org/articles/10.5802/jedp.625/}
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Mattingly, Jonathan. On recent progress for the stochastic Navier Stokes equations. Journées équations aux dérivées partielles (2003), article  no. 11, 52 p. doi : 10.5802/jedp.625. http://www.numdam.org/articles/10.5802/jedp.625/

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