A parabolic toy-model for the incompressible Navier–Stokes system is considered. This model shares a lot of similar features with the incompressible model, including the energy inequality, the scaling symmetry, and it is also supercritical in 3D. A 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. A Caffarelli–Kohn–Nirenberg type result for the model is also proved in a direct manner. Finally, the absence of divergence-free constraint allows us to study this model in the radially symmetric setting for which full regularity is established.
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Published in Zapiski Nauchnykh Seminarov POMI, Vol. 489, 2020, pp. 173–206.
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Hounkpe, F. On a Toy-Model Related to the Navier–Stokes Equations. J Math Sci 260, 118–141 (2022). https://doi.org/10.1007/s10958-021-05677-9
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DOI: https://doi.org/10.1007/s10958-021-05677-9