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The Stokes Resolvent Problem in General Unbounded Domains (Kyoto Conference on the Navier-Stokes Equations and their Applications)
| Content Provider | Semantic Scholar |
|---|---|
| Author | Farwig, Reinhard Kozono, Hideo Sohr, Hermann |
| Copyright Year | 2007 |
| Abstract | It is well-known that the Helmholtz decomposition of Lq-spaces fails to exist for certain unbounded smooth domains unless q = 2. Hence also the Stokes operator is not well-defined for these domains when q 6= 2. In this paper, we generalize a new approach to the Stokes problem in general unbounded smooth domains from the three-dimensional case, see [5], to the n-dimensional one, n ≥ 2, replacing the space Lq, 1 < q < ∞, by Lq where Lq = Lq ∩ L2 for q ≥ 2 and Lq = Lq + L2 for 1 < q < 2. In particular, we show that the Stokes operator is well-defined in Lq for every unbounded domain of uniform C1,1-type in Rn, n ≥ 2, and generates an analytic semigroup. 2000 Mathematics Subject Classification: Primary 76D05, Secondary 35Q30 |
| Starting Page | 79 |
| Ending Page | 91 |
| Page Count | 13 |
| File Format | PDF HTM / HTML |
| Volume Number | 1 |
| Alternate Webpage(s) | http://www.kurims.kyoto-u.ac.jp/~kenkyubu/bessatsu/open/B1/pdf/B01_005.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
