Probabilistic global well-posedness for a viscous nonlinear wave equation modeling fluid–structure interaction

@article{Kuan2022ProbabilisticGW,
  title={Probabilistic global well-posedness for a viscous nonlinear wave equation modeling fluid–structure interaction},
  author={Jeffrey Kuan and Tadahiro Oh and Sun{\vc}ica {\vC}ani{\'c}},
  journal={Applicable Analysis},
  year={2022},
  volume={101},
  pages={4349 - 4373}
}
We prove probabilistic well-posedness for a 2D viscous nonlinear wave equation modeling fluid–structure interaction between a 3D incompressible, viscous Stokes flow and nonlinear elastodynamics of a 2D stretched membrane. The focus is on (rough) data, often arising in real-life problems, for which it is known that the deterministic problem is ill-posed. We show that random perturbations of such data give rise almost surely to the existence of a unique solution. More specifically, we prove… 
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