On the interaction of an elasticwall with a poiseuille-type flow
We study the dynamics of a coupled system formed by the 3D Navier–Stokes equations linearized near a certain Poiseuille-type flow in an (unbounded) domain and a classical (possibly nonlinear) equation for transverse displacements of an elastic plate in a flexible flat part of the boundary. We first...
Збережено в:
| Дата: | 2013 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2013
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| Назва видання: | Український математичний журнал |
| Теми: | |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/164930 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | On the interaction of an elasticwall with a poiseuille-type flow / I. Chueshov, I. Ryzhkova // Український математичний журнал. — 2013. — Т. 65, № 1. — С. 143-160. — Бібліогр.: 35 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Резюме: | We study the dynamics of a coupled system formed by the 3D Navier–Stokes equations linearized near a certain Poiseuille-type flow in an (unbounded) domain and a classical (possibly nonlinear) equation for transverse displacements of an elastic plate in a flexible flat part of the boundary. We first show that this problem generates an evolution semigroup St in an appropriate phase space. Then, under some conditions imposed on the underlying (Poiseuille-type) flow, we prove the existence of a compact finite-dimensional global attractor for this semigroup and also show that St is an exponentially stable C₀ -semigroup of linear operators in the completely linear case. Since we do not assume any kind of mechanical damping in the plate component, this means that the dissipation of energy in the flow of fluid caused by viscosity is sufficient to stabilize the system. |
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