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Linearized Navier-Stokes equations in $\mathbb{R}^3$: An approach in weighted Sobolev spaces
1. | Laboratoire de Mathématiques et de leurs Applications, CNRS UMR 5142, Université de Pau et des Pays de l'Adour, 64013 Pau, France, France |
2. | Mathematical Institute, Academy of Sciences of the Czech Republic, Žitná 25, 115 67 Praha 1 |
References:
[1] |
F. Alliot and C. Amrouche, The Stokes problem in $\mathbbR^n$: An approach in weighted Sobolev spaces, Math. Mod. Meth. Appl. Sci., 9 (1999), 723-754.
doi: 10.1142/S0218202599000361. |
[2] |
C. Amrouche and L. Consiglieri, On the stationary Oseen equations in $\mathbbR^{3}$, Communications in Mathematical Analysis, 10 (2011), 5-29. |
[3] |
C. Amrouche, V. Girault and J. Giroire, Weighted Sobolev spaces for the laplace equation in $\mathbbR^n$, J. Math. Pures et Appl., 73 (1994), 579-606. |
[4] |
C. Amrouche and M. A. Rodriguez-Bellido, Stationary Stokes, Oseen and Navier-Stokes equations with singular data, Archive for Rational Mechanics and Analysis, 199 (2011), 597-651.
doi: 10.1007/s00205-010-0340-8. |
[5] |
M. Cantor, Spaces of functions with asymptotic conditions on $\mathbbR^n$, Indiana Univ. Math. J., 24 (1975), 897-902. |
[6] |
R. Farwig, The stationary exterior 3D-problem of Oseen and Navier-Stokes equations in anisotropically weighted Sobolev spaces, Math. Z, 211 (1992), 409-447.
doi: 10.1007/BF02571437. |
[7] |
R. Farwig, The stationary Navier-Stokes equations in a 3D-exterior domain, in Recent Topics on Mathematical Theory of Viscous Incompressible Fluid (Tsukuba, 1996), Lecture Notes Numer. Appl. Anal., 16, Kinokuniya, Tokyo, 1998, 53-115. |
[8] |
G. P. Galdi, An Introduction to the Mathematical Theory of the Navier-Stokes Equations. Vol. I. Linearized Steady Problems, Springer Tracts in Natural Philosophy, 38, Springer-Verlag, New York, 1994. |
[9] |
G. P. Galdi, An Introduction to the Mathematical Theory of the Navier-Stokes Equations. Vol. II. Nonlinear Steady Problems, Springer Tracts in Natural Philosophy, 39, Springer-Verlag, New York, 1994. |
[10] |
B. Hanouzet, Espace de Sobolev avec poids. Application au problème de Dirichlet dans un demi espace, Rend. Sem. Mat. Univ. Padova, 46 (1971), 227-272. |
show all references
References:
[1] |
F. Alliot and C. Amrouche, The Stokes problem in $\mathbbR^n$: An approach in weighted Sobolev spaces, Math. Mod. Meth. Appl. Sci., 9 (1999), 723-754.
doi: 10.1142/S0218202599000361. |
[2] |
C. Amrouche and L. Consiglieri, On the stationary Oseen equations in $\mathbbR^{3}$, Communications in Mathematical Analysis, 10 (2011), 5-29. |
[3] |
C. Amrouche, V. Girault and J. Giroire, Weighted Sobolev spaces for the laplace equation in $\mathbbR^n$, J. Math. Pures et Appl., 73 (1994), 579-606. |
[4] |
C. Amrouche and M. A. Rodriguez-Bellido, Stationary Stokes, Oseen and Navier-Stokes equations with singular data, Archive for Rational Mechanics and Analysis, 199 (2011), 597-651.
doi: 10.1007/s00205-010-0340-8. |
[5] |
M. Cantor, Spaces of functions with asymptotic conditions on $\mathbbR^n$, Indiana Univ. Math. J., 24 (1975), 897-902. |
[6] |
R. Farwig, The stationary exterior 3D-problem of Oseen and Navier-Stokes equations in anisotropically weighted Sobolev spaces, Math. Z, 211 (1992), 409-447.
doi: 10.1007/BF02571437. |
[7] |
R. Farwig, The stationary Navier-Stokes equations in a 3D-exterior domain, in Recent Topics on Mathematical Theory of Viscous Incompressible Fluid (Tsukuba, 1996), Lecture Notes Numer. Appl. Anal., 16, Kinokuniya, Tokyo, 1998, 53-115. |
[8] |
G. P. Galdi, An Introduction to the Mathematical Theory of the Navier-Stokes Equations. Vol. I. Linearized Steady Problems, Springer Tracts in Natural Philosophy, 38, Springer-Verlag, New York, 1994. |
[9] |
G. P. Galdi, An Introduction to the Mathematical Theory of the Navier-Stokes Equations. Vol. II. Nonlinear Steady Problems, Springer Tracts in Natural Philosophy, 39, Springer-Verlag, New York, 1994. |
[10] |
B. Hanouzet, Espace de Sobolev avec poids. Application au problème de Dirichlet dans un demi espace, Rend. Sem. Mat. Univ. Padova, 46 (1971), 227-272. |
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