Asymptotic stability of finite energy in Navier Stokes-elastic wave interaction
Asymptotic stability of finite energy in Navier Stokes-elastic wave interaction
复制标题
纳维斯托克斯-弹性波相互作用中有限能量的渐近稳定性
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
Yongjin Lu
中科院分区：
文献类型：
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作者：
I. Lasiecka;Yongjin Lu
我们考虑有界域Ω∈ℝ2中的流固耦合模型，其中Ω由两个开放的相邻子域组成，分别由固体和流体占据。这就引出了耦合到弹性动力系统界面上的纳维斯托克斯方程的研究。该耦合模型的特点是预解不紧，表征总能量平衡的能量函数弱退化。再加上缺乏机械耗散和动力学固有的非线性，使得渐近稳定性的问题变得相当微妙。事实上，唯一的耗散来源是流体通过界面传播的粘性效应。结果表明，在适当的几何条件下，当时间t收敛到无穷大时，与弱解有关的有限能量函数收敛到零。所需的几何条件源于作用在固体上的压力的存在。
We consider a model of fluid-structure interaction in a bounded domain Ω∈ℝ2 where Ω is comprised of two open adjacent sub-domains occupied, respectively, by the solid and the fluid. This leads to a study of Navier Stokes equation coupled on the interface to the dynamic system of elasticity. The characteristic feature of this coupled model is that the resolvent is not compact and the energy function characterizing balance of the total energy is weakly degenerated. These combined with the lack of mechanical dissipation and intrinsic nonlinearity of the dynamics render the problem of asymptotic stability rather delicate. Indeed, the only source of dissipation is the viscosity effect propagated from the fluid via interface. It will be shown that under suitable geometric conditions imposed on the geometry of the interface, finite energy function associated with weak solutions converges to zero when the time t converges to infinity. The required geometric conditions result from the presence of the pressure acting upon the solid.