Existence of time-periodic weak solutions is proved for the coupled Navier-Stokes and nonlinear Koiter plate system in a space-periodic moving domain using a single Leray-Schauder fixed-point argument on the Galerkin system.
Time-periodic solutions for hyperbolic-parabolic systems
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Polynomial semigroup stability implies periodic well-posedness on a dense set of forcings whose time-derivative loss is controlled by resolvent bounds.
Links non-uniform energy decay in free damped systems to existence of periodic solutions under periodic forcing, while relating resolvent growth to regularity loss, with illustrations from damped wave equations and a resonance counterexample.
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Time-periodic solutions for viscous fluids interacting with nonlinear Koiter plates
Existence of time-periodic weak solutions is proved for the coupled Navier-Stokes and nonlinear Koiter plate system in a space-periodic moving domain using a single Leray-Schauder fixed-point argument on the Galerkin system.
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Periodic solutions for weakly damped systems
Links non-uniform energy decay in free damped systems to existence of periodic solutions under periodic forcing, while relating resolvent growth to regularity loss, with illustrations from damped wave equations and a resonance counterexample.