About the behavior of regular Navier-Stokes solutions near the bow up
About the behavior of regular Navier-Stokes solutions near the bow up
![About the behavior of regular Navier-Stokes solutions near the bow up](https://smf.emath.fr/sites/default/files/styles/image_165x234/public/2018-12/Titre_04_Poulon_0.jpg?itok=keUN6Oxa)
Anglais
In this paper, we present some results about blow up of regular solutions to the homogeneous incompressible Navier-Stokes system, in the case of data in the Sobolev space $\dot{H}^{s}(\mathbb{R}^3)$, where~${\frac{1}{2} < s < \frac{3}{2}} \cdotp$ Firstly, we will introduce the notion of minimal blow up Navier-Stokes solutions and show that the set of such solutions is not only nonempty but also compact in a certain sense. Secondly, we will state an uniform blow up rate for minimal Navier-Stokes solutions. The key tool is profile theory as established by P. Gérard.
Navier-Stokes equations, blow up, profile decomposition