[Existence locale et unicité de solutions de l'équation d'Euler hydrostatique dans un ouvert borné avec des données analytiques]
On étudie le caractère bien posé dans des espaces de fonctions analytiques de l'équation d'Euler hydrostatique pour un fluide incompressible (équations primitives non-visqueuses) sur des domaines à bords, avec une nouvelle condition de bord.
We address the question of well-posedness in spaces of analytic functions for the hydrostatic incompressible Euler equations (inviscid primitive equations) on domains with boundary, with a novel side-boundary condition.
Accepté le :
Publié le :
@article{CRMATH_2010__348_11-12_639_0,
author = {Kukavica, Igor and Temam, Roger and Vicol, Vlad and Ziane, Mohammed},
title = {Existence and uniqueness of solutions for the hydrostatic {Euler} equations on a bounded domain with analytic data},
journal = {Comptes Rendus. Math\'ematique},
pages = {639--645},
publisher = {Elsevier},
volume = {348},
number = {11-12},
year = {2010},
doi = {10.1016/j.crma.2010.03.023},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2010.03.023/}
}
TY - JOUR AU - Kukavica, Igor AU - Temam, Roger AU - Vicol, Vlad AU - Ziane, Mohammed TI - Existence and uniqueness of solutions for the hydrostatic Euler equations on a bounded domain with analytic data JO - Comptes Rendus. Mathématique PY - 2010 SP - 639 EP - 645 VL - 348 IS - 11-12 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2010.03.023/ DO - 10.1016/j.crma.2010.03.023 LA - en ID - CRMATH_2010__348_11-12_639_0 ER -
%0 Journal Article %A Kukavica, Igor %A Temam, Roger %A Vicol, Vlad %A Ziane, Mohammed %T Existence and uniqueness of solutions for the hydrostatic Euler equations on a bounded domain with analytic data %J Comptes Rendus. Mathématique %D 2010 %P 639-645 %V 348 %N 11-12 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2010.03.023/ %R 10.1016/j.crma.2010.03.023 %G en %F CRMATH_2010__348_11-12_639_0
Kukavica, Igor; Temam, Roger; Vicol, Vlad; Ziane, Mohammed. Existence and uniqueness of solutions for the hydrostatic Euler equations on a bounded domain with analytic data. Comptes Rendus. Mathématique, Tome 348 (2010) no. 11-12, pp. 639-645. doi : 10.1016/j.crma.2010.03.023. http://www.numdam.org/articles/10.1016/j.crma.2010.03.023/
[1] Domaine d'analycité des solutions de l'équation d'Euler dans un ouvert de , Ann. Sc. Norm. Super. Pisa Cl. Sci. (4), Volume 4 (1977), pp. 647-687
[2] Analyticité des solutions périodiques de l'équation d'Euler en deux dimensions, C. R. Acad. Sci. Paris Sér. A–B, Volume 282 (1976) no. 17, p. A995-A998 (Aiii)
[3] Homogeneous hydrostatic flows with convex velocity profiles, Nonlinearity, Volume 12 (1999), pp. 495-512
[4] On the derivation of homogeneous hydrostatic equations, M2AN Math. Model. Numer. Anal., Volume 33 (1999) no. 5, pp. 965-970
[5] On the radius of analyticity of solutions to the three-dimensional Euler equations, Proc. Amer. Math. Soc., Volume 137 (2009), pp. 669-677
[6] I. Kukavica, V. Vicol, The domain of analyticity of solutions to the three-dimensional Euler equations in a half space, Discrete Contin. Dyn. Syst. Ser. A, in press
[7] I. Kukavica, R. Temam, V. Vicol, M. Ziane, Local existence and uniqueness for the hydrostatic Euler equations on a bounded domain, preprint
[8] Mathematical Topics in Fluid Mechanics, vol. 1. Incompressible Models, Oxford Lecture Ser. Math. Appl., vol. 3, Oxford University Press, New York, 1996
[9] New formulations of the primitive equations of atmosphere and applications, Nonlinearity, Volume 5 (1992) no. 2, pp. 237-288
[10] Analyticity of solutions for a generalized Euler equation, J. Differential Equations, Volume 133 (1997) no. 2, pp. 321-339
[11] Well-posedness of the boundary layer equations, SIAM J. Math. Anal., Volume 35 (2003) no. 4, pp. 987-1004
[12] Geophysical Fluid Dynamics, Springer-Verlag, New York, 1987
[13] Ill-posedness of the hydrostatic Euler and Navier–Stokes equations, Arch. Ration. Mech. Anal., Volume 194 (2009), pp. 877-886
[14] Boundary conditions for the 2D linearized PEs of the ocean in the absence of viscosity, Discrete Contin. Dyn. Syst. Ser. A, Volume 13 (2005) no. 5, pp. 1257-1276
[15] The 3D primitive equations in the absence of viscosity: Boundary conditions and well-posedness in the linearized case, J. Math. Pures Appl., Volume 89 (2008), pp. 297-319
[16] Theoretical and practical aspects of some initial boundary value problems in fluid dynamics, SIAM J. Appl. Math., Volume 35 (1978) no. 3, pp. 419-446
[17] Zero viscosity limit for analytic solutions of the Navier–Stokes equation on a half-space, I. Existence for Euler and Prandtl equations, Comm. Math. Phys., Volume 192 (1998), pp. 433-461
[18] On the Euler equations of incompressible perfect fluids, J. Funct. Anal., Volume 20 (1975) no. 1, pp. 32-43
[19] Some mathematical problems in geophysical fluid dynamics, Handbook of Mathematical Fluid Dynamics, vol. III, North-Holland, Amsterdam, 2004, pp. 535-657
Cité par Sources :
