Geodesic
Navier-Stokes equations on unbounded domains with rough initial data
Czechoslovak Mathematical Journal, Tome 60 (2010) no. 2, pp. 297-313 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

We consider the Navier-Stokes equations in unbounded domains $\Omega \subseteq \mathbb R ^n$ of uniform $C^{1,1}$-type. We construct mild solutions for initial values in certain extrapolation spaces associated to the Stokes operator on these domains. Here we rely on recent results due to Farwig, Kozono and Sohr, the fact that the Stokes operator has a bounded $H^\infty $-calculus on such domains, and use a general form of Kato's method. We also obtain information on the corresponding pressure term.
We consider the Navier-Stokes equations in unbounded domains $\Omega \subseteq \mathbb R ^n$ of uniform $C^{1,1}$-type. We construct mild solutions for initial values in certain extrapolation spaces associated to the Stokes operator on these domains. Here we rely on recent results due to Farwig, Kozono and Sohr, the fact that the Stokes operator has a bounded $H^\infty $-calculus on such domains, and use a general form of Kato's method. We also obtain information on the corresponding pressure term.
Classification : 35K55, 35Q30, 76D05
Keywords: Navier-Stokes equations; mild solutions; Stokes operator; extrapolation spaces; $H^\infty $-functional calculus; general unbounded domains; pressure term 
@article{CMJ_2010_60_2_a0,
     author = {Kunstmann, Peer Christian},
     title = {Navier-Stokes equations on unbounded domains with rough initial data},
     journal = {Czechoslovak Mathematical Journal},
     pages = {297--313},
     year = {2010},
     volume = {60},
     number = {2},
     mrnumber = {2657950},
     zbl = {1224.35319},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2010_60_2_a0/}
}
TY  - JOUR
AU  - Kunstmann, Peer Christian
TI  - Navier-Stokes equations on unbounded domains with rough initial data
JO  - Czechoslovak Mathematical Journal
PY  - 2010
SP  - 297
EP  - 313
VL  - 60
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/CMJ_2010_60_2_a0/
LA  - en
ID  - CMJ_2010_60_2_a0
ER  - 
%0 Journal Article
%A Kunstmann, Peer Christian
%T Navier-Stokes equations on unbounded domains with rough initial data
%J Czechoslovak Mathematical Journal
%D 2010
%P 297-313
%V 60
%N 2
%U http://geodesic.mathdoc.fr/item/CMJ_2010_60_2_a0/
%G en
%F CMJ_2010_60_2_a0
Kunstmann, Peer Christian. Navier-Stokes equations on unbounded domains with rough initial data. Czechoslovak Mathematical Journal, Tome 60 (2010) no. 2, pp. 297-313. http://geodesic.mathdoc.fr/item/CMJ_2010_60_2_a0/