Lp-theory for the Navier-Stokes equations with pressure boundary conditions

Chérif Amrouche (1) , N. El Houda Seloula

1 LMAP - Laboratoire de Mathématiques et de leurs Applications [Pau]

We consider the Navier-Stokes equations with pressure boundary conditions in the case of a bounded open set, connected of class C 1;1 of ℝ3. We prove existence of solution by using a fixed point theorem over the type-Oseen problem. This result was studied in [5] in the Hilbertian case. In our study we give the Lp-theory for 1 < p < ∞.

Domaines: Equations aux dérivées partielles [math.AP]

Chérif Amrouche, N. El Houda Seloula. Lp-theory for the Navier-Stokes equations with pressure boundary conditions. Discrete and Continuous Dynamical Systems - Series S, 2013, 6 (5), pp.1113-1137. ⟨10.3934/dcdss.2013.6.1113⟩. ⟨hal-00866944⟩