A stability of the steady flow of compressible viscous fluid with respect to initial disturbance (v∞ ≠ 0)
✍ Scribed by Koumei Tanaka
- Publisher
- John Wiley and Sons
- Year
- 2006
- Tongue
- English
- Weight
- 154 KB
- Volume
- 29
- Category
- Article
- ISSN
- 0170-4214
- DOI
- 10.1002/mma.502
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✦ Synopsis
We consider a compressible viscous uid with the velocity at inÿnity equal to a strictly non-zero constant vector in R 3 . Under the assumptions on the smallness of the external force and velocity at inÿnity, Novotny-Padula (Math. Ann. 1997; 308:439-489) proved the existence and uniqueness of steady ow in the class of functions possessing some pointwise decay. In this paper, we study stability of the steady ow with respect to the initial disturbance. We proved that if H 3 -norm of the initial disturbance is small enough, then the solution to the non-stationary problem exists uniquely and globally in time, which satisÿes a uniform estimate on prescribed velocity at inÿnity and converges to the steady ow in Lq-norm for any number q¿2.