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Various boundary conditions for Navier-Stokes equations in bounded Lipschitz domains
1. | Sylvie Monniaux - LATP CMI Université Aix-Marseille, 39 rue Frédéric Joliot-Curie, 13453 Marseille Cedex 13, France |
References:
[1] |
Paul Deuring, The Stokes resolvent in 3D domains with conical boundary points: Nonregularity in $L^p$-spaces, Adv. Differential Equations, 6 (2001), 175-228. |
[2] |
Paul Deuring and Wolf von Wahl, Strong solutions of the Navier-Stokes system in Lipschitz bounded domains, Math. Nachr., 171 (1995), 111-148.
doi: 10.1002/mana.19951710108. |
[3] |
Eugene Fabes, Osvaldo Mendez and Marius Mitrea, Boundary layers on Sobolev-Besov spaces and Poisson's equation for the Laplacian in Lipschitz domains, J. Funct. Anal., 159 (1998), 323-368.
doi: 10.1006/jfan.1998.3316. |
[4] |
Hiroshi Fujita and Tosio Kato, On the Navier-Stokes initial value problem. I, Arch. Rational Mech. Anal., 16 (1964), 269-315. |
[5] |
Yoshikazu Giga, Analyticity of the semigroup generated by the Stokes operator in $L_r$ spaces, Math. Z., 178 (1981), 297-329.
doi: 10.1007/BF01214869. |
[6] |
Yoshikazu Giga and Tetsuro Miyakawa, Solutions in $L_r$ of the Navier-Stokes initial value problem, Arch. Rational Mech. Anal., 89 (1985), 267-281.
doi: 10.1007/BF00276875. |
[7] |
Alf Jonsson and Hans Wallin, Function spaces on subsets of $R^n$, Math. Rep., 2 (1984), xiv+221. |
[8] |
Jacques-Louis Lions, Espaces d'interpolation et domaines de puissances fractionnaires d'opérateurs, J. Math. Soc. Japan, 14 (1962), 233-241. |
[9] |
Dorina Mitrea, Marius Mitrea and Sylvie Monniaux, The Poisson problem for the exterior derivative operator with Dirichlet boundary condition in nonsmooth domains, Commun. Pure Appl. Anal., 7 (2008), 1295-1333.
doi: 10.3934/cpaa.2008.7.1295. |
[10] |
Dorina Mitrea, Marius Mitrea and Michael Taylor, Layer potentials, the Hodge Laplacian, and global boundary problems in nonsmooth Riemannian manifolds, Mem. Amer. Math. Soc., 150 (2001), x+120. |
[11] |
Marius Mitrea and Sylvie Monniaux, The regularity of the Stokes operator and the Fujita-Kato approach to the Navier-Stokes initial value problem in Lipschitz domains, J. Funct. Anal., 254 (2008), 1522-1574.
doi: 10.1016/j.jfa.2007.11.021. |
[12] |
Marius Mitrea and Sylvie Monniaux, On the analyticity of the semigroup generated by the Stokes operator with Neumann-type boundary conditions on Lipschitz subdomains of Riemannian manifolds, Trans. Amer. Math. Soc., 361 (2009), 3125-3157.
doi: 10.1090/S0002-9947-08-04827-7. |
[13] |
Marius Mitrea and Sylvie Monniaux, The nonlinear Hodge-Navier-Stokes equations in Lipschitz domains, Differential Integral Equations, 22 (2009), 339-356. |
[14] |
Marius Mitrea, Sylvie Monniaux and Matthew Wright, The Stokes operator with Neumann boundary conditions in Lipschitz domains, J. Math. Sci. (N. Y.), 176 (2011), 409-457.
doi: 10.1007/s10958-011-0400-0. |
[15] |
Sylvie Monniaux, On uniqueness for the Navier-Stokes system in 3D-bounded Lipschitz domains, J. Funct. Anal., 195 (2002), 1-11.
doi: 10.1006/jfan.2002.3902. |
[16] |
Sylvie Monniaux, Navier-Stokes equations in arbitrary domains: The Fujita-Kato scheme, Math. Res. Lett., 13 (2006), 455-461. |
[17] |
Sylvie Monniaux, Maximal regularity and applications to PDEs, in "Analytical and Numerical Aspects of Partial Differential Equations," Walter de Gruyter, Berlin, (2009), 247-287. |
[18] |
Michael E. Taylor, Incompressible fluid flows on rough domains, in "Semigroups of Operators: Theory and Applications" (Newport Beach, CA, 1998), Progr. Nonlinear Differential Equations Appl., 42, Birkhäuser, Basel, 2000, 320-334. |
show all references
References:
[1] |
Paul Deuring, The Stokes resolvent in 3D domains with conical boundary points: Nonregularity in $L^p$-spaces, Adv. Differential Equations, 6 (2001), 175-228. |
[2] |
Paul Deuring and Wolf von Wahl, Strong solutions of the Navier-Stokes system in Lipschitz bounded domains, Math. Nachr., 171 (1995), 111-148.
doi: 10.1002/mana.19951710108. |
[3] |
Eugene Fabes, Osvaldo Mendez and Marius Mitrea, Boundary layers on Sobolev-Besov spaces and Poisson's equation for the Laplacian in Lipschitz domains, J. Funct. Anal., 159 (1998), 323-368.
doi: 10.1006/jfan.1998.3316. |
[4] |
Hiroshi Fujita and Tosio Kato, On the Navier-Stokes initial value problem. I, Arch. Rational Mech. Anal., 16 (1964), 269-315. |
[5] |
Yoshikazu Giga, Analyticity of the semigroup generated by the Stokes operator in $L_r$ spaces, Math. Z., 178 (1981), 297-329.
doi: 10.1007/BF01214869. |
[6] |
Yoshikazu Giga and Tetsuro Miyakawa, Solutions in $L_r$ of the Navier-Stokes initial value problem, Arch. Rational Mech. Anal., 89 (1985), 267-281.
doi: 10.1007/BF00276875. |
[7] |
Alf Jonsson and Hans Wallin, Function spaces on subsets of $R^n$, Math. Rep., 2 (1984), xiv+221. |
[8] |
Jacques-Louis Lions, Espaces d'interpolation et domaines de puissances fractionnaires d'opérateurs, J. Math. Soc. Japan, 14 (1962), 233-241. |
[9] |
Dorina Mitrea, Marius Mitrea and Sylvie Monniaux, The Poisson problem for the exterior derivative operator with Dirichlet boundary condition in nonsmooth domains, Commun. Pure Appl. Anal., 7 (2008), 1295-1333.
doi: 10.3934/cpaa.2008.7.1295. |
[10] |
Dorina Mitrea, Marius Mitrea and Michael Taylor, Layer potentials, the Hodge Laplacian, and global boundary problems in nonsmooth Riemannian manifolds, Mem. Amer. Math. Soc., 150 (2001), x+120. |
[11] |
Marius Mitrea and Sylvie Monniaux, The regularity of the Stokes operator and the Fujita-Kato approach to the Navier-Stokes initial value problem in Lipschitz domains, J. Funct. Anal., 254 (2008), 1522-1574.
doi: 10.1016/j.jfa.2007.11.021. |
[12] |
Marius Mitrea and Sylvie Monniaux, On the analyticity of the semigroup generated by the Stokes operator with Neumann-type boundary conditions on Lipschitz subdomains of Riemannian manifolds, Trans. Amer. Math. Soc., 361 (2009), 3125-3157.
doi: 10.1090/S0002-9947-08-04827-7. |
[13] |
Marius Mitrea and Sylvie Monniaux, The nonlinear Hodge-Navier-Stokes equations in Lipschitz domains, Differential Integral Equations, 22 (2009), 339-356. |
[14] |
Marius Mitrea, Sylvie Monniaux and Matthew Wright, The Stokes operator with Neumann boundary conditions in Lipschitz domains, J. Math. Sci. (N. Y.), 176 (2011), 409-457.
doi: 10.1007/s10958-011-0400-0. |
[15] |
Sylvie Monniaux, On uniqueness for the Navier-Stokes system in 3D-bounded Lipschitz domains, J. Funct. Anal., 195 (2002), 1-11.
doi: 10.1006/jfan.2002.3902. |
[16] |
Sylvie Monniaux, Navier-Stokes equations in arbitrary domains: The Fujita-Kato scheme, Math. Res. Lett., 13 (2006), 455-461. |
[17] |
Sylvie Monniaux, Maximal regularity and applications to PDEs, in "Analytical and Numerical Aspects of Partial Differential Equations," Walter de Gruyter, Berlin, (2009), 247-287. |
[18] |
Michael E. Taylor, Incompressible fluid flows on rough domains, in "Semigroups of Operators: Theory and Applications" (Newport Beach, CA, 1998), Progr. Nonlinear Differential Equations Appl., 42, Birkhäuser, Basel, 2000, 320-334. |
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