About the behavior of regular Navier-Stokes solutions near the bow up
About the behavior of regular Navier-Stokes solutions near the bow up
Bulletin de la SMF | 2018

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- Année : 2018
- Fascicule : 2
- Tome : 146
- Format : Électronique
- Langue de l'ouvrage :
Anglais - Pages : 355-390
- DOI : 10.24033/bsmf.2760
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