Study of Anisotropic MHD system in Anisotropic Sobolev spaces

Jamel Ben Ameur[1]; Ridha Selmi[2]

  • [1] Faculté des Sciences de Bizerte, Tunisie
  • [2] Institut Supérieur d’Informatique, l’Ariana 2080, Tunisie

Annales de la faculté des sciences de Toulouse Mathématiques (2008)

  • Volume: 17, Issue: 1, page 1-22
  • ISSN: 0240-2963

Abstract

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Three-dimensional anisotropic magneto-hydrodynamical system is investigated in the whole space ℝ 3 . Existence and uniqueness results are proved in the anisotropic Sobolev space H 0 , s for s > 1 / 2 . Asymptotic behavior of the solution when the Rossby number goes to zero is studied. The proofs, where the incompressibility condition is crucial, use the energy method, an appropriate dyadic decomposition of the frequency space, product laws in anisotropic Sobolev spaces and Strichartz-type estimates.

How to cite

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Ben Ameur, Jamel, and Selmi, Ridha. "Study of Anisotropic MHD system in Anisotropic Sobolev spaces." Annales de la faculté des sciences de Toulouse Mathématiques 17.1 (2008): 1-22. <http://eudml.org/doc/10077>.

@article{BenAmeur2008,
abstract = {Three-dimensional anisotropic magneto-hydrodynamical system is investigated in the whole space $\mathbb\{R\}^3$. Existence and uniqueness results are proved in the anisotropic Sobolev space $H^\{0,s\}$ for $s&gt;1/2$. Asymptotic behavior of the solution when the Rossby number goes to zero is studied. The proofs, where the incompressibility condition is crucial, use the energy method, an appropriate dyadic decomposition of the frequency space, product laws in anisotropic Sobolev spaces and Strichartz-type estimates.},
affiliation = {Faculté des Sciences de Bizerte, Tunisie; Institut Supérieur d’Informatique, l’Ariana 2080, Tunisie},
author = {Ben Ameur, Jamel, Selmi, Ridha},
journal = {Annales de la faculté des sciences de Toulouse Mathématiques},
keywords = {energy method; dyadic decomposition; Strichartz estimates},
language = {eng},
month = {6},
number = {1},
pages = {1-22},
publisher = {Université Paul Sabatier, Toulouse},
title = {Study of Anisotropic MHD system in Anisotropic Sobolev spaces},
url = {http://eudml.org/doc/10077},
volume = {17},
year = {2008},
}

TY - JOUR
AU - Ben Ameur, Jamel
AU - Selmi, Ridha
TI - Study of Anisotropic MHD system in Anisotropic Sobolev spaces
JO - Annales de la faculté des sciences de Toulouse Mathématiques
DA - 2008/6//
PB - Université Paul Sabatier, Toulouse
VL - 17
IS - 1
SP - 1
EP - 22
AB - Three-dimensional anisotropic magneto-hydrodynamical system is investigated in the whole space $\mathbb{R}^3$. Existence and uniqueness results are proved in the anisotropic Sobolev space $H^{0,s}$ for $s&gt;1/2$. Asymptotic behavior of the solution when the Rossby number goes to zero is studied. The proofs, where the incompressibility condition is crucial, use the energy method, an appropriate dyadic decomposition of the frequency space, product laws in anisotropic Sobolev spaces and Strichartz-type estimates.
LA - eng
KW - energy method; dyadic decomposition; Strichartz estimates
UR - http://eudml.org/doc/10077
ER -

References

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  7. Iftimie (D.).— Resolution of the Navier-Stokes Equations in Anisotropic Spaces, Revista Matemática Iberoamericana, 15, no. 1, p. 1-36, (1999). Zbl0923.35119MR1681635
  8. Iftimie (D.).— A uniqueness Result for the Navier-Stokes Equations with Vanishing Vertical Viscosity, SIAM J. MATH. ANAL, 33, no. 6, p. 1483-1493, (2002). Zbl1011.35105MR1920641
  9. Lions (J.-L.) and Magenes (E.).— Problème aux Limites Non Homogènes et Applications. Vol. 1 Dunod, Paris, 1968. Zbl0165.10801MR247243
  10. Pedlosky (J.).— Geophysical Fluid Dynamics, Springer Verlag, New York, 1987. Zbl0713.76005
  11. Selmi (R.).— Convergence Results for MHD System, International Journal of Mathematics and Mathematical Sciences 2006 (2006), Article ID 28704, 19 pages. Zbl1127.35050MR2251633

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