Geodesic
On a toy-model related to the Navier–Stokes equations
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 48, Tome 489 (2020), pp. 173-206 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper, we consider a parabolic toy-model for the incompressible Navier–Stokes system. This model, as we shall see below, shares a lot of similar features with the incompressible model; among which the energy inequality, the scaling symmetry, and it is also supercritical in $3$D. Our goal is to establish some regularity results for this toy-model in order to get, if possible, better insight to the standard Navier–Stokes system. We also prove here, in a direct manner, a Caffarelli–Kohn–Nirenberg type result for our model. Finally, taking advantage of the absence of the divergence-free constraint, we are able to study this model in the radially symmetric setting for which we are able to establish full regularity. 
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     title = {On a toy-model related to the {Navier{\textendash}Stokes} equations},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2020_489_a8/}
}
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F. Hounkpe. On a toy-model related to the Navier–Stokes equations. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 48, Tome 489 (2020), pp. 173-206. http://geodesic.mathdoc.fr/item/ZNSL_2020_489_a8/

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