| Abstract: |
| In this talk I will present our recent result on the global existence of weak solutions of a fluid structure interaction problem involving two Newtonian incompressible heat conducting fluids separated by an elastic plate/ shell. The elastic plate involved allows heat transfer between the two fluids. We show the global existence of weak solution to our model until the Koiter energy degenerates or the structure undergoes a self intersection or touches the rigid boundary $\partial\Omega$. The two fluids involved are assumed to have different viscosities and they depend on the respective temperatures. The temperature dependence of the viscosities is modeled by the celebrated Vogel-Fulcher-Tammann equation. We use a variational strategy in order to construct weak solutions which involves regularization of the Koiter energy, adding artificial dissipation and discretization using two different time scales: velocity scale and the acceleration scale. |
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