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I would need to get acquainted to the subject of stochastic Stokes flows, so studying Stokes equations under some noise of some kind, let's say an additive white noise to begin with.

The problem is that Navier-Stokes equations are likely THE most studied equations out there, there's a gazillion articles popping up if I look for "Stochastic Stokes equation".

I would be ok even with some basic stuff, just to get started with, it would be better to also have some relevant nontrivial (whatever that means) work from where I can start looking at references in that article and other works referencing that. I mean, I'd really like some suggestions for some starting points.

P.S. I think I can find the treatment of deterministic Stokes flow, basically every book about Navier-Stokes will have a part about that, I guess. What I'd need is the stochastic case

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In the 2d-case a lot of results have been proved already: see textbook by Sergei Kuksin, Armen Shirikyan "Mathematics of Two-Dimensional Turbulence" (see equation 2.100 for Stochastic Stokes).

In terms of SPDEs in general, one introduction that is often referenced is by Giuseppe Da Prato and Jerzy Zabczy "Stochastic Equations in Infinite Dimensions". It contains many references for stochastic Navier Stokes too see chapter "13.11 Navier–Stokes equations and hydrodynamics".

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  • $\begingroup$ Thanks! I knew the book by Da Prato, but didn't know about the references therein. In the book by Kuksin and Shirikyan I don't see any particular focus on Stokes (just had a quick glampse though), does that mean they only treat the more general Navier-Stokes equations and the Stokes case can just be treated as a particular case? $\endgroup$
    – tommy1996q
    Commented Aug 29, 2023 at 16:18
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    $\begingroup$ see equation 2.100 for Stochastic Stokes $\endgroup$
    – Thomas Kojar
    Commented Aug 29, 2023 at 16:41

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