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

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

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

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
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