Some examples of global solutions associated with large initial data for the incompressible Navier Stokes system
56
pages
English
Documents
Obtenez un accès à la bibliothèque pour le consulter en ligne En savoir plus
Découvre YouScribe en t'inscrivant gratuitement
Découvre YouScribe en t'inscrivant gratuitement
56
pages
English
Documents
Obtenez un accès à la bibliothèque pour le consulter en ligne En savoir plus
Some examples of global solutions associated with large initial data for the incompressible Navier-Stokes system Isabelle Gallagher Institut de Mathematiques de Jussieu, Universite Paris 7 Luminy, March 25, 2008 I. Gallagher (IMJ, Paris 7) Examples of large solutions to Navier-Stokes Luminy, March 25, 2008 1 / 22
Voir
- largest adapted space
- solution associated
- weak solution
- navier-stokes luminy
- tataru space
- divergence-free vector
Isabelle Gallagher
Luminy, March 25, 2008
InstitutdeMathe´matiquesdeJussieu,Universit´eParis7
Some examples of global solutions associated with large initial data for the incompressible Navier-Stokes system
char,22581002/2
The Cauchy problem Presentation of the equations Fundamental properties Weak solutions Strong solutions Towards the largest adapted space The Koch and Tataru space
1
Outline of the talk
Situations when large data can generate a global solution Previous results Two examples
2
nstoNavier-StokeLsmuni,yaMcr2h,5
∂tu+u∙ ru−Δu=−rp divu= 0
(NS)
gesolutilesoflarei-rtSkonotsNovaar,M25chLuesnymi
3 withdivu=X∂jujandu∙ ru=Xuj∂ju=X∂j(uju). j=1j=1j=1 Remark :The pressure can be eliminated byprojection onto divergence-free vector fields:
Presentation of the equations
2
P= Id− rΔ−1div.
•Viscous, incompressible, homogeneous fluid, in two or three space dimensions
•Velocityu= (u1u2u3)(tx), pressurep(tx)
Cauchy data :u|t=0=u0.
002,2/3833s7)ExampIMJ,Parillgaeh(r.IaG
P= Id− rΔ−1div.
∂tu+u∙ ru−Δu=−rp divu= 0
(NS)
3 withdivu=X∂jujandu∙ ru=Xuj∂ju=X∂j(uju). j=1j=1j=1 Remark :The pressure can be eliminated byprojection onto divergence-free vector fields:
Cauchy data :u|t=0=u0.
•Velocityu= (u1u2u3)(tx), pressurep(tx)
•Viscous, incompressible, homogeneous fluid, in two or three space dimensions
22
Presentation of the equations
083/02,52hcraM,ynimusLketo-ServiNato
3 withdivu=X∂jujandu∙ ru=Xuj∂ju=X∂j(uju). j=1j=1j=1 Remark :The pressure can be eliminated byprojection onto divergence-free vector fields:
Presentation of the equations
•Velocityu= (u1u2u3)(tx), pressurep(tx)
Cauchy data :u|t=0=u0.
2/2
P= Id− rΔ−1div.
•Viscous, incompressible, homogeneous fluid, in two or three space dimensions
(NS)
∂tu+u∙ ru−Δu=−rp divu= 0
archny,M008325,2
