Very weak solutions for the stationary 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 consider the stationary Oseen and Navier-Stokes equations in a bounded domain of class $C^{1,1}$ of $R^3$. Here we give a new and simpler proof of the existence of very weak solutions $(u, q) \in L^p(\Omega) × W^{−1,p}(\Omega)$ corresponding to boundary data in $W^{−1/p,p}(\Gamma)$. These solutions are obtained without imposing smallness assumptions on the exterior forces. We also obtain regularity results in fractional Sobolev spaces.

Domaines: Equations aux dérivées partielles [math.AP]

Chérif Amrouche, M.A. Rodriguez-Bellido. Very weak solutions for the stationary Oseen and Navier-Stokes equations.. Comptes Rendus. Mathématique, 2010, 348 (5-6), pp.335-339. ⟨hal-00444235⟩