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Dive into the research topics where Chérif Amrouche is active.

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Featured researches published by Chérif Amrouche.


Siam Journal on Mathematical Analysis | 2000

Pointwise decay of solutions and of higher derivatives to Navier-Stokes equations

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

Lp-theory for vector potentials and sobolev's inequalities for vector fields: Application to the stokes equations with pressure boundary conditions

Chérif Amrouche; Nour El Houda Seloula

2\le n \le 5


Comptes Rendus Mathematique | 2002

The Neumann problem in the half-space

Chérif Amrouche

. Using moment estimates...


Mathematical Methods in The Applied Sciences | 2000

Weak solutions for the exterior Stokes problem in weighted Sobolev spaces

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

ON THE OSEEN PROBLEM IN THREE-DIMENSIONAL EXTERIOR DOMAINS

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

New estimates for the div, curl, grad operators and elliptic problems with L-1-data in the half-space

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

FROM STRONG TO VERY WEAK SOLUTIONS TO THE STOKES SYSTEM WITH NAVIER BOUNDARY CONDITIONS IN THE HALF-SPACE

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

Weighted estimates for the Oseen problem in R 3

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

Isotropically and Anisotropically Weighted Sobolev Spaces for the Oseen Equation

Chérif Amrouche; Ulrich Razafison

We consider the Stokes problem with slip-type boundary conditions in the half-space


Archive | 2002

On the Regularity and Decay of the Weak Solutions to the Steady-State Navier-Stokes Equations in Exterior Domains

Frédéric Alliot; Chérif Amrouche

\mathbb{R}^n_+

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Ulrich Razafison

University of Franche-Comté

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Philippe G. Ciarlet

City University of Hong Kong

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Yves Raudin

Centre national de la recherche scientifique

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Šárka Nečasová

Academy of Sciences of the Czech Republic

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Hamid Bouzit

University of Mostaganem

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Ahmed Rejaiba

Centre national de la recherche scientifique

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Huy Hoang Nguyen

Centre national de la recherche scientifique

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Macaire Batchi

Centre national de la recherche scientifique

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Mohamed Meslameni

Centre national de la recherche scientifique

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