Chérif Amrouche
Centre national de la recherche scientifique
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Featured researches published by Chérif Amrouche.
Siam Journal on Mathematical Analysis | 2000
Chérif Amrouche; Vivette Girault; Maria E. Schonbek; Thomas P. Schonbek
In this paper we study the space-time asymptotic behavior of the solutions, and their derivatives, to the incompressible Navier--Stokes equations in dimension
Mathematical Models and Methods in Applied Sciences | 2013
Chérif Amrouche; Nour El Houda Seloula
2\le n \le 5
Comptes Rendus Mathematique | 2002
Chérif Amrouche
. Using moment estimates...
Mathematical Methods in The Applied Sciences | 2000
Frédéric Alliot; Chérif Amrouche
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.
Analysis and Applications | 2006
Chérif Amrouche; Ulrich Razafison
We study here the nonhomogeneous Neumann problem in the half-space RN+ with N⩾2. We give in Lp theory, with 1<p<∞, a basic existence and regularity results in weighted Sobolev spaces. To cite this article: C. Amrouche, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 151–156.
Applied Mathematics Letters | 2011
Chérif Amrouche; Huy Hoang Nguyen
We extend here some existence and uniqueness results for the exterior Stokes problem in weighted Sobolev spaces. We also study the regularity of the solutions (u, π) and prove optimal a priori estimates for the solutions with ⊇ 2 u, ⊇π ∈ L p . The influence of some compatibility conditions on the behaviour at infinity of the solution is finally studied and leads to new asymptotic expansions.
Siam Journal on Mathematical Analysis | 2009
Chérif Amrouche; Šárka Nečasová; Yves Raudin
In this paper, we prove existence and uniqueness results for the Oseen problem in exterior domains of ℝ3. To prescribe the growth or decay of functions at infinity, we set the problem in weighted Sobolev spaces. The analysis relies on a Lp-theory for any real p such that 1 < p < ∞.
Applied Mathematics Letters | 2006
Chérif Amrouche; Ulrich Razafison
Abstract In this Note, we study some properties of the div, curl, grad operators and elliptic problems in the half-space. We consider data in weighted Sobolev spaces and in L 1 .
Archive | 2009
Chérif Amrouche; Ulrich Razafison
We consider the Stokes problem with slip-type boundary conditions in the half-space
Archive | 2002
Frédéric Alliot; Chérif Amrouche
\mathbb{R}^n_+