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Journals and Conferences
We deal with the Laplace equation in the half space. The use of a special family of weigted Sobolev spaces as a framework is at the heart of our approach. A complete class of existence, uniqueness and regularity results is obtained for inhomogeneous Dirichlet problem.
Saint Venant’s and Donati’s theorems constitute two classical characterizations of smooth matrix fields as linearized strain tensor fields. Donati’s characterization has been extended to matrix fields with components in L by T. W. Ting in 1974 and by J. J. Moreau in 1979, and Saint Venant’s characterization has been extended likewise by the second author… (More)
In this Note, we present several results concerning vector potentials and scalar potentials in a bounded, not necessarily simply-connected, three-dimensional domain. In particular, we consider singular potentials corresponding to data in negative order Sobolev spaces. We also give some applications to Poincaré’s theorem and to Korn’s inequality.
We establish here some existence and uniqueness properties for the exterior Stokes problem with prescribed growth or decay at innnity for the solutions. For this purpose, the problem is set in some suitable weighted Sobolev spaces. We also obtain an asymptotic expansion for some well behaved solutions. Consider an open region of R n. In the sequel, we shall… (More)
In a possibly multiply-connected three dimensional bounded domain, we prove in the Lp theory the existence and uniqueness of vector potentials, associated with a divergence-free function and satisfying non homogeneous boundary conditions. Furthermore, we consider the stationary Stokes equations with nonstandard boundary conditions of the form u · n = g and… (More)
In this Note, we present some existence results of the Oseen equations set in R3 proved in a previous work. In order to control the behavior at infinity of functions, we use as functional framework weighted Sobolev spaces. The asymptotic of some solutions is then studied. © 2005 Elsevier Ltd. All rights reserved.
We present in this note the existence and uniqueness results for the Stokes and Navier-Stokes equations which model the laminar flow of an incompressible fluid inside a two-dimensional channel of periodic sections. The data of the pressure loss coefficient enables us to establish a relation on the pressure and to thus formulate an equivalent problem.
We consider the Stokes problem with slip type boundary conditions in the half-space R+, with n > 2. The weighted Sobolev spaces yield the functional framework. We study generalized and strong solutions and then the case with very low regularity of data on the boundary. We apply the method of decomposition introduced in our previous work (see ), where it… (More)
We consider the stationary Oseen and Navier-Stokes equations in a bounded domain of class C of R. Here we give a new and simpler proof of the existence of very weak solutions (u , q) ∈ L(Ω) × W−1,p(Ω) corresponding to boundary data in W−1/p,p(Γ). These solutions are obtained without imposing smallness assumptions on the exterior forces. We also obtain… (More)