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.