Asymptotics and stability for global solutions to the

Isabelle Gallagher

Description

Niveau: Supérieur, Doctorat, Bac+8
Asymptotics and stability for global solutions to the Navier-Stokes equations Isabelle Gallagher a Drago? Iftimie a;b Fabrice Planchon c Abstract We consider an a priori global strong solution to the Navier-Stokes equations. We prove it behaves like a small solution for large time. Combining this asymptotics with uniqueness and averaging in time properties, we obtain the stability of such a global solution. Introduction We consider the incompressible Navier-Stokes equations in R 3 , (1) 8 > < > : @u @t = ur (u u)r; r u = 0; u(x; 0) = u 0 (x): There exist essentially two dierent kinds of results on the Cauchy problem for these equations. In the pioneering work [15], Jean Leray introduced the concept of weak solutions and proved global existence for datum u 0 2 L 2 . However, their uniqueness (or propagation/breakdown of regularity for smooth data) has remained an open problem. In [11], H. Fujita and T. Kato obtained solutions for datum u 0 2 _ H 1 2 by semi-group methods.

• global solution


• weak solution


• then


• local space-time


• global strong


• existence then


• blow-up time


• there exists

Sujets

• Gallagher
• Planchon
• Weak solution
• Existential quantification

Informations

• Publié par: profil-zyak-2012
• Nombre de lectures: 23
• Langue: English

Extrait

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