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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{ZNSL_2020_489_a8,
     author = {F. Hounkpe},
     title = {On a toy-model related to the {Navier--Stokes} equations},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {173--206},
     publisher = {mathdoc},
     volume = {489},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2020_489_a8/}
}
TY  - JOUR
AU  - F. Hounkpe
TI  - On a toy-model related to the Navier--Stokes equations
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2020
SP  - 173
EP  - 206
VL  - 489
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2020_489_a8/
LA  - en
ID  - ZNSL_2020_489_a8
ER  - 
%0 Journal Article
%A F. Hounkpe
%T On a toy-model related to the Navier--Stokes equations
%J Zapiski Nauchnykh Seminarov POMI
%D 2020
%P 173-206
%V 489
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ZNSL_2020_489_a8/
%G en
%F ZNSL_2020_489_a8
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/