SELOULA, Nour El Houda; AMROUCHE, Chérif

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SELOULA, Nour El Houda
Équipe Calcul scientifique et Modélisation

AMROUCHE, Chérif
Laboratoire de Mathématiques et de leurs Applications [Pau] [LMAP]

Langue

Document de travail - Pré-publication

Résumé en anglais

In a three dimensional bounded possibly multiply-connected domain, we give gradient and higher order estimates of vector fields via div and curl in Lp theory. Then, we prove the existence and uniqueness of vector potentials, associated with a divergence-free function and satisfying some boundary conditions. We also present some results concerning scalar potentials and weak vector potentials. Furthermore, we consider the stationary Stokes equations with nonstandard boundary conditions of the form u × n = g × n and π = π0 on the boundary Γ. We prove the existence and uniqueness of weak, strong and very weak solutions. Our proofs are based on obtaining Inf − Sup conditions that play a fundamental role. We give a variant of the Stokes system with these boundary conditions, in the case where the compatibility condition is not verified. Finally, we give two Helmholtz decompositions that consist of two kinds of boundary conditions such as u * n and u × n on Γ.< Réduire

Mots clés en anglais

Vector Potentials

boundary conditions

Stokes

Helmholtz decomposition

Inf-Sup condition

Sobolev inequality.

Sobolev inequality

Origine

Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251