The scalar Oseen operator - Δ + ∂ / ∂ x 1 in ℝ 2

Chérif Amrouche; Hamid Bouzit

Applications of Mathematics (2008)

  • Volume: 53, Issue: 1, page 41-80
  • ISSN: 0862-7940

Abstract

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This paper solves the scalar Oseen equation, a linearized form of the Navier-Stokes equation. Because the fundamental solution has anisotropic properties, the problem is set in a Sobolev space with isotropic and anisotropic weights. We establish some existence results and regularities in L p theory.

How to cite

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Amrouche, Chérif, and Bouzit, Hamid. "The scalar Oseen operator $-\Delta + {\partial }/{\partial x_1}$ in $\mathbb {R}^2$." Applications of Mathematics 53.1 (2008): 41-80. <http://eudml.org/doc/33310>.

@article{Amrouche2008,
abstract = {This paper solves the scalar Oseen equation, a linearized form of the Navier-Stokes equation. Because the fundamental solution has anisotropic properties, the problem is set in a Sobolev space with isotropic and anisotropic weights. We establish some existence results and regularities in $L^\{p\}$ theory.},
author = {Amrouche, Chérif, Bouzit, Hamid},
journal = {Applications of Mathematics},
keywords = {Oseen equation; weighted Sobolev space; anisotropic weight; Oseen equation; weighted Sobolev space; anisotropic weight},
language = {eng},
number = {1},
pages = {41-80},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The scalar Oseen operator $-\Delta + \{\partial \}/\{\partial x_1\}$ in $\mathbb \{R\}^2$},
url = {http://eudml.org/doc/33310},
volume = {53},
year = {2008},
}

TY - JOUR
AU - Amrouche, Chérif
AU - Bouzit, Hamid
TI - The scalar Oseen operator $-\Delta + {\partial }/{\partial x_1}$ in $\mathbb {R}^2$
JO - Applications of Mathematics
PY - 2008
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 53
IS - 1
SP - 41
EP - 80
AB - This paper solves the scalar Oseen equation, a linearized form of the Navier-Stokes equation. Because the fundamental solution has anisotropic properties, the problem is set in a Sobolev space with isotropic and anisotropic weights. We establish some existence results and regularities in $L^{p}$ theory.
LA - eng
KW - Oseen equation; weighted Sobolev space; anisotropic weight; Oseen equation; weighted Sobolev space; anisotropic weight
UR - http://eudml.org/doc/33310
ER -

References

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