## FARWIG Reinhard, KOZONO Hideo, SOHR Hermann,

## On the stokes operator in general unbounded domains.

## Hokkaido Mathematical Journal, 38 (2009) pp.111-136

### Fulltext

PDF### Abstract

It is known that the Stokes operator is not well-defined in $L^q$-spaces for certain unbounded smooth domains unless $q=2$.
In this paper, we generalize a new approach to the Stokes resolvent problem and to maximal regularity
in general unbounded smooth domains from the three-dimensional case, see \cite{FKS1}, to the $n$-dimensional one, $n\geq 2$,
replacing the space $L^q, 1

MSC(Primary) | 76D05 |
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MSC(Secondary) | 35Q30 |

Uncontrolled Keywords | General unbounded domains, domains of uniform C^{1,1}-type, Stokes operator, Stokes resolvent, Stokes semigroup, maximal regularity |