ON THE VERY WEAK SOLUTION FOR THE OSEEN AND NAVIER-STOKES EQUATIONS

Chérif Amrouche (1) , M.A. Rodriguez-Bellido (2)

1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]
2 EDAN - Departamento de Ecuaciones Differenciales y Analysis numérico [Sevilla]

We study the existence of very weak solutions regularity for the Stokes, Oseen and Navier-Stokes system when non-smooth Dirichlet boundary data for the velocity are considered in domains of class C1,1. In the Navier-Stokes case, the results will be valid for external forces non necessarily small. Regularity results for more regular data will be also discussed.

Mots clés: Stokes equations; Oseen equations; Navier-Stokes equations; Very weak solutions; Stationary Solutions

Domaines: Equations aux dérivées partielles [math.AP]

Chérif Amrouche, M.A. Rodriguez-Bellido. ON THE VERY WEAK SOLUTION FOR THE OSEEN AND NAVIER-STOKES EQUATIONS. 2010. ⟨hal-00549173⟩