About the behavior of regular Navier-Stokes solutions near the bow up
About the behavior of regular Navier-Stokes solutions near the bow up

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 ˙Hs(R3), where~12<s<32⋅ 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