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A stability of the steady flow of compressible viscous fluid with respect to initial disturbance ( v ∞ ≠ 0)
Author(s) -
Tanaka Koumei
Publication year - 2006
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.502
Subject(s) - mathematics , pointwise , uniqueness , compressibility , infinity , compressible flow , mathematical analysis , flow (mathematics) , norm (philosophy) , disturbance (geology) , uniform norm , mechanics , geometry , physics , paleontology , political science , law , biology
We consider a compressible viscous fluid with the velocity at infinity equal to a strictly non‐zero constant vector in ℝ 3 . Under the assumptions on the smallness of the external force and velocity at infinity, Novotny–Padula ( Math . Ann . 1997; 308 :439– 489) proved the existence and uniqueness of steady flow in the class of functions possessing some pointwise decay. In this paper, we study stability of the steady flow 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 satisfies a uniform estimate on prescribed velocity at infinity and converges to the steady flow in L q ‐norm for any number q ⩾ 2. Copyright © 2006 John Wiley & Sons, Ltd.