LP -THEORY FOR VECTOR POTENTIALS AND SOBOLEV'S INEQUALITIES FOR VECTOR FIELDS. APPLICATION TO THE STOKES EQUATIONS WITH PRESSURE BOUNDARY CONDITIONS
Idioma
en
Document de travail - Pré-publication
Resumen en inglés
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, ...Leer más >
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.< Leer menos
Palabras clave en inglés
Vector Potentials
boundary conditions
Stokes
Helmholtz decomposition
Inf-Sup condition
Sobolev inequality.
Sobolev inequality
Orígen
Importado de HalCentros de investigación