The 3D time-dependent Oseen system: link between L p -integrability in time and pointwise decay in space of the velocity

Paul Deuring (1)

1 LMPA - Laboratoire de Mathématiques Pures et Appliquées Joseph Liouville

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

Mots clés: integral representation; decay; Oseen system

Domaines: Equations aux dérivées partielles [math.AP]

Paul Deuring. The 3D time-dependent Oseen system: link between L p -integrability in time and pointwise decay in space of the velocity. 2020. ⟨hal-02465649v2⟩