Strong well-posedness of a fluid--poro-viscoelastic interaction problem: An approach by Spectral analysis

This article investigates a coupled viscoelastic Navier–Stokes–Biot system describing the interaction between an incompressible viscous fluid and a poro–viscoelastic medium in three spatial dimensions. The coupling between the fluid and the porous medium is realized through Beavers–Joseph–Saffman type interface conditions. Using spectral analysis, it is proved that the coupled system admits a unique, strong, global solution for small initial data. In addition, a Serrin–type blow-up criterion is established.