| Title:
|
Maximal regularity of the spatially periodic Stokes operator and application to nematic liquid crystal flows (English) |
| Author:
|
Sauer, Jonas |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
66 |
| Issue:
|
1 |
| Year:
|
2016 |
| Pages:
|
41-55 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We consider the dynamics of spatially periodic nematic liquid crystal flows in the whole space and prove existence and uniqueness of local-in-time strong solutions using maximal $L^p$-regularity of the periodic Laplace and Stokes operators and a local-in-time existence theorem for quasilinear parabolic equations à la Clément-Li (1993). Maximal regularity of the Laplace and the Stokes operator is obtained using an extrapolation theorem on the locally compact abelian group $G:=\mathbb R^{n-1}\times \mathbb R / L \mathbb Z$ to obtain an $\mathcal {R}$-bound for the resolvent estimate. Then, Weis' theorem connecting $\mathcal {R}$-boundedness of the resolvent with maximal $L^p$ regularity of a sectorial operator applies. (English) |
| Keyword:
|
Stokes operator |
| Keyword:
|
spatially periodic problem |
| Keyword:
|
maximal $L^p$ regularity |
| Keyword:
|
nematic liquid crystal flow |
| Keyword:
|
quasilinear parabolic equations |
| MSC:
|
35B10 |
| MSC:
|
35K59 |
| MSC:
|
35Q35 |
| MSC:
|
76A15 |
| MSC:
|
76D03 |
| idZBL:
|
Zbl 06587871 |
| idMR:
|
MR3483220 |
| DOI:
|
10.1007/s10587-016-0237-2 |
| . |
| Date available:
|
2016-04-07T14:51:15Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144878 |
| . |
| Reference:
|
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