| Abstract: |
| In this talk, we will consider a fluid-structure interaction problem involving a viscous, incompressible fluid flow, modeled by the 2D Navier-Stokes equations, through a thin deformable elastic tube, elastodynamics of which is modeled by 1D plate equations. The fluid and the structure are nonlinearly coupled at the fluid-structure interface. The fluid flow is driven by dynamic pressure data imposed at the inlet and the outlet of the tube. In this talk, we will impose the Navier-slip boundary condition at the fluid-structure interface and at the bottom rigid boundary of the fluid domain. We will first discuss the existence of weak solutions and reveal a `hidden' spatial regularity result for the structure displacement.
Then we will discuss our recent result that establishes the existence of a finite time for the weak solutions at which the compliant upper boundary meets the lower boundary (i.e., the tube collapses), provided that there is a sufficient pressure drop across the channel. This resolves the ``no-collision'' paradox identified in the no-slip setting and thus validates the model to correctly capture near-contact dynamics. |
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