Advances in Differential Equations

Reflection principles and kernels in $\mathbb R^n_+$ for the biharmonic and Stokes operators. Solutions in a large class of weighted Sobolev spaces

Chérif Amrouche and Yves Raudin

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Abstract

In this paper, we study the Stokes system in the half-space $\mathbb{R}^n_+$, with $n {\geqslant} 2$. We consider data and give solutions which live in weighted Sobolev spaces, for a whole scale of weights. We start to study the kernels of the biharmonic and Stokes operators. After the central case of the generalized solutions, we are interested in strong solutions and symmetrically in very weak solutions by means of a duality argument.

Article information

Source
Adv. Differential Equations Volume 15, Number 3/4 (2010), 201-230.

Dates
First available in Project Euclid: 18 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355854748

Mathematical Reviews number (MathSciNet)
MR2588448

Zentralblatt MATH identifier
1193.35030

Subjects
Primary: 35J50: Variational methods for elliptic systems 35J55 35Q30: Navier-Stokes equations [See also 76D05, 76D07, 76N10] 76D07: Stokes and related (Oseen, etc.) flows 76N10: Existence, uniqueness, and regularity theory [See also 35L60, 35L65, 35Q30]

Citation

Amrouche, Chérif; Raudin, Yves. Reflection principles and kernels in $\mathbb R^n_+$ for the biharmonic and Stokes operators. Solutions in a large class of weighted Sobolev spaces. Adv. Differential Equations 15 (2010), no. 3/4, 201--230. https://projecteuclid.org/euclid.ade/1355854748.


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