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Decay estimates of the Stokes flow around a rotating obstacle(Kyoto Conference on the Navier-Stokes Equations and their Applications)
| Content Provider | Semantic Scholar |
|---|---|
| Author | Hishida, Toshiaki Shibata, Yoshihiro |
| Copyright Year | 2007 |
| Abstract | We study the motion of a viscous incompressible fluid filling the whole 3‐dimensional space exterior to a rigid body that is rotating with con‐ stant angular velocity $\omega$ . By using a frame attached to the body, the problem is reduced to an equivalent one in a fixed exterior domain. Then the linear part of the reduced equation is \partial_{t}u=\triangle u+( $\omega$\times x)\cdot\nabla u$\omega$\times u-\nabla p, \mathrm{d}\mathrm{i}\mathrm{v}u=0. For the exterior problem with the Dirichlet boundary condition, we develop the L_{p}-L_{q} estimates (and the L_{p,1}-L_{q,1} estimates as well) of the generated semigroup, which is no longer analytic due to the drift operator with the coefficient $\omega$\times x . We next apply them to the Navier‐ Stokes equation to prove the global existence of a unique solution which goes to a stationary flow as t\rightarrow\infty with some definite rates when both the stationary flow and the initial disturbance are sufficiently small in L_{3,\infty} ( \mathrm{w}\mathrm{e}\mathrm{a}\mathrm{k}-L_{3} space). |
| Starting Page | 167 |
| Ending Page | 186 |
| Page Count | 20 |
| File Format | PDF HTM / HTML |
| Volume Number | 1 |
| Alternate Webpage(s) | http://www.kurims.kyoto-u.ac.jp/~kenkyubu/bessatsu/open/B1/pdf/B01_011.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
