کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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4609520 | 1338516 | 2016 | 37 صفحه PDF | دانلود رایگان |
We investigate stability of an equilibrium state to a nonhomogeneous incompressible viscoelastic fluid driven by gravity in a bounded domain Ω⊂R3Ω⊂R3 of class C3C3. First, we establish a critical number κCκC, which depends on the equilibrium density and the gravitational constant, and is a threshold of the elasticity coefficient κ for instability and stability of the linearized perturbation problem around the equilibrium state. Then we prove that the equilibrium state is exponential stability provided that κ>κCκ>κC and the initial disturbance quantities around the equilibrium state satisfy some relations. In particular, if the equilibrium density ρ¯ is a Rayleigh–Taylor (RT) type and ρ¯′ is a constant, our result strictly shows that the sufficiently large elasticity coefficient can prevent the RT instability from occurrence.
Journal: Journal of Differential Equations - Volume 260, Issue 10, 15 May 2016, Pages 7498–7534