On a Toy-Model related to the Navier-Stokes Equations
arXiv:2003.06392 · doi:10.1007/s10958-021-05677-9
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 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.
To appear in "Journal of Mathematical Sciences"