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Abstract:

If Ω ⊂ n is a bounded domain, the existence of solutions u∈ H10(Ω)n of div u = f for f ∈ L 2(Ω) with vanishing mean value, is a basic result in the analysis of the Stokes equations. In particular, it allows to show the existence of a solution (u,p)∈ H10(Ω)n× L2(Ω ), where u is the velocity and p the pressure. It is known that the above-mentioned result holds when Ω is a Lipschitz domain and that it is not valid for arbitrary Hölder-α domains. In this paper we prove that if Ω is a planar simply connected Hölder-α domain, there exist solutions of div u = f in appropriate weighted Sobolev spaces, where the weights are powers of the distance to the boundary. Moreover, we show that the powers of the distance in the results obtained are optimal. For some particular domains with an external cusp, we apply our results to show the well-posedness of the Stokes equations in appropriate weighted Sobolev spaces obtaining as a consequence the existence of a solution (u,p)∈ H10(Ω) n× Lr(Ω) for some r < 2 depending on the power of the cusp. © 2010 World Scientific Publishing Company.

Registro:

Documento: Artículo
Título:Solutions of the divergence and analysis of the stokes equations in planar Hölder-α domains
Autor:DurÁn, R.G.; López GarcÍa, F.
Filiación:Departamento de Matemática, Facultad de Ciencias Exactas, Físicas y Naturales, Universidad de Buenos Aires, 1428 Buenos Aires, Argentina
Palabras clave:Divergence operator; Hölder-α domains; Stokes equations; Basic results; Bounded domain; Divergence operators; Existence of Solutions; Lipschitz domain; Mean values; Stokes equations; Weighted Sobolev spaces; Wellposedness; Holmium; Sobolev spaces; Mathematical operators
Año:2010
Volumen:20
Número:1
Página de inicio:95
Página de fin:120
DOI: http://dx.doi.org/10.1142/S0218202510004167
Título revista:Mathematical Models and Methods in Applied Sciences
Título revista abreviado:Math. Models Methods Appl. Sci.
ISSN:02182025
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_02182025_v20_n1_p95_DurAn

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Citas:

---------- APA ----------
DurÁn, R.G. & López GarcÍa, F. (2010) . Solutions of the divergence and analysis of the stokes equations in planar Hölder-α domains. Mathematical Models and Methods in Applied Sciences, 20(1), 95-120.
http://dx.doi.org/10.1142/S0218202510004167
---------- CHICAGO ----------
DurÁn, R.G., López GarcÍa, F. "Solutions of the divergence and analysis of the stokes equations in planar Hölder-α domains" . Mathematical Models and Methods in Applied Sciences 20, no. 1 (2010) : 95-120.
http://dx.doi.org/10.1142/S0218202510004167
---------- MLA ----------
DurÁn, R.G., López GarcÍa, F. "Solutions of the divergence and analysis of the stokes equations in planar Hölder-α domains" . Mathematical Models and Methods in Applied Sciences, vol. 20, no. 1, 2010, pp. 95-120.
http://dx.doi.org/10.1142/S0218202510004167
---------- VANCOUVER ----------
DurÁn, R.G., López GarcÍa, F. Solutions of the divergence and analysis of the stokes equations in planar Hölder-α domains. Math. Models Methods Appl. Sci. 2010;20(1):95-120.
http://dx.doi.org/10.1142/S0218202510004167