The 3D Time-Dependent Oseen System: Link Between $$L^p$$-Integrability in Time and Pointwise Decay in Space of the Velocity

A representation formula without pressure term is derived for regular solutions to the 3D time-dependent Oseen system in exterior Lipschitz domains. This valid even if no boundary conditions are imposed. It used order exhibit how velocity decays pointwise space. turns out that rate of this decay depends on $$L^p$$ -integrability time velocity. In addition, work basis successor papers dealing with spatial $$L^q$$ -weak and mild system, $$L^2$$ -strong stability problem related Navier-Stokes term.