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Fractional stochastic active scalar equations generalizing the multi-dimensional quasi-geostrophic & 2D-Navier-Stokes equations: the general case. (English) Zbl 1467.58017

In this paper the author is investigating the well-posedness, the uniqueness and the regularity of the solutions of a class of d-dimensional fractional stochastic active scalar equations defined either on the torus \(\mathbb{T}^{d}\) or \(\mathbb{R}^{d}\) or \(O\) bounded. A lot of functional analytic tools is used in order to handle many statements. The paper is very comprehensive. It contains 52 pages and the bibliography contains 118 references. The article seems to be selfcontained and most of statements are proven in detail.

MSC:

58J65 Diffusion processes and stochastic analysis on manifolds
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
35R11 Fractional partial differential equations
35Q30 Navier-Stokes equations
46B25 Classical Banach spaces in the general theory
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References:

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