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Zapiski Nauchnykh Seminarov POMI, 2020, Volume 489, Pages 173–206
(Mi znsl6920)
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On a toy-model related to the Navier–Stokes equations
F. Hounkpe Mathematical Institute, University of Oxford, Oxford, UK
Abstract:
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.
Key words and phrases:
suitable weak solutions, partial regularity, radial symmetry.
Received: 06.12.2019
Citation:
F. Hounkpe, “On a toy-model related to the Navier–Stokes equations”, Boundary-value problems of mathematical physics and related problems of function theory. Part 48, Zap. Nauchn. Sem. POMI, 489, POMI, St. Petersburg, 2020, 173–206
Linking options:
https://www.mathnet.ru/eng/znsl6920 https://www.mathnet.ru/eng/znsl/v489/p173
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Statistics & downloads: |
Abstract page: | 105 | Full-text PDF : | 28 | References: | 25 |
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