Spatial asymptotics of mild solutions to the time-dependent Oseen system

Paul Deuring (1, 2)

1 LMPA - Laboratoire de Mathématiques Pures et Appliquées Joseph Liouville
2 ULCO - Université du Littoral Côte d'Opale

We consider mild solutions to the 3D time-dependent Oseen system with homogeneous Dirichlet boundary conditions, under weak assumptions on the data. Such solutions are defined via the semigroup generated by the Oseen operator in L^q. They turn out to be also L^q-weak solutions to the Oseen system. On the basis of known results about spatial asymptotics of the latter type of solutions, we then derive point-wise estimates of the spatial decay of mild solutions. The rate of decay depends in particular on L^p-integrability in time of the external force.

Mots clés: 35D30 Key words Oseen system; mild solution; spatial decay; Oseen semigroup; AMS subject classifications 35Q35; 76D07; 35B40

Domaines: Equations aux dérivées partielles [math.AP]

Paul Deuring. Spatial asymptotics of mild solutions to the time-dependent Oseen system. 2022. ⟨hal-02546017v2⟩