Existence and regularity of weak solutions for a fluid interacting with a non-linear shell in three dimensions

We study the unsteady incompressible Navier-Stokes equations in three dimensions interacting with a non-linear flexible shell of Koiter type. This leads to coupled system PDEs where moving part boundary is an unknown problem. The known existence theory for weak solutions extended models. introduce a-priori estimates that reveal higher regularity displacement beyond energy estimates. These are essential models, since such models non-convex (w.r.t.\ terms highest order). obtained by introducing new analytical tools allow exploit dissipative effects fluid (non-dissipative) solid. result depends on geometric constitution alone and independent approximation procedure; hence it holds arbitrary solutions. developed further used generalized Aubin-Lions type compactness suitable fluid-structure interactions.