Navier-Stokes equations on unbounded domains with rough initial data

Peer Christian Kunstmann

Czechoslovak Mathematical Journal (2010)

  • Volume: 60, Issue: 2, page 297-313
  • ISSN: 0011-4642

Abstract

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We consider the Navier-Stokes equations in unbounded domains Ω ⊆ 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 ∞ -calculus on such domains, and use a general form of Kato’s method. We also obtain information on the corresponding pressure term.

How to cite

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Kunstmann, Peer Christian. "Navier-Stokes equations on unbounded domains with rough initial data." Czechoslovak Mathematical Journal 60.2 (2010): 297-313. <http://eudml.org/doc/38008>.

@article{Kunstmann2010,
abstract = {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.},
author = {Kunstmann, Peer Christian},
journal = {Czechoslovak Mathematical Journal},
keywords = {Navier-Stokes equations; mild solutions; Stokes operator; extrapolation spaces; $H^\infty $-functional calculus; general unbounded domains; pressure term; Navier-Stokes equations; mild solution; Stokes operator; extrapolation space; -functional calculus; general unbounded domain; pressure term},
language = {eng},
number = {2},
pages = {297-313},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Navier-Stokes equations on unbounded domains with rough initial data},
url = {http://eudml.org/doc/38008},
volume = {60},
year = {2010},
}

TY - JOUR
AU - Kunstmann, Peer Christian
TI - Navier-Stokes equations on unbounded domains with rough initial data
JO - Czechoslovak Mathematical Journal
PY - 2010
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 60
IS - 2
SP - 297
EP - 313
AB - 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.
LA - eng
KW - Navier-Stokes equations; mild solutions; Stokes operator; extrapolation spaces; $H^\infty $-functional calculus; general unbounded domains; pressure term; Navier-Stokes equations; mild solution; Stokes operator; extrapolation space; -functional calculus; general unbounded domain; pressure term
UR - http://eudml.org/doc/38008
ER -

References

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