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Vanishing viscosity limit for an expanding domain in space

James P. Kelliher; Milton C. Lopes Filho; Helena J. Nussenzveig Lopes

Annales de l'I.H.P. Analyse non linéaire (2009)

  • Volume: 26, Issue: 6, page 2521-2537
  • ISSN: 0294-1449

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Kelliher, James P., Filho, Milton C. Lopes, and Lopes, Helena J. Nussenzveig. "Vanishing viscosity limit for an expanding domain in space." Annales de l'I.H.P. Analyse non linéaire 26.6 (2009): 2521-2537. <http://eudml.org/doc/78946>.

@article{Kelliher2009,
author = {Kelliher, James P., Filho, Milton C. Lopes, Lopes, Helena J. Nussenzveig},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {inviscid limit; vanishing viscosity limit; Navier-Stokes equations; Euler equations},
language = {eng},
number = {6},
pages = {2521-2537},
publisher = {Elsevier},
title = {Vanishing viscosity limit for an expanding domain in space},
url = {http://eudml.org/doc/78946},
volume = {26},
year = {2009},
}

TY - JOUR
AU - Kelliher, James P.
AU - Filho, Milton C. Lopes
AU - Lopes, Helena J. Nussenzveig
TI - Vanishing viscosity limit for an expanding domain in space
JO - Annales de l'I.H.P. Analyse non linéaire
PY - 2009
PB - Elsevier
VL - 26
IS - 6
SP - 2521
EP - 2537
LA - eng
KW - inviscid limit; vanishing viscosity limit; Navier-Stokes equations; Euler equations
UR - http://eudml.org/doc/78946
ER -

References

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  1. [1] Chemin Jean-Yves, Perfect Incompressible Fluids, Oxford Lecture Ser. Math. Appl., vol. 14, Clarendon Press, Oxford University Press, New York, 1998, translated from the 1995 French original by Isabelle Gallagher and Dragos Iftimie. Zbl0927.76002
  2. [2] DiPerna Ronald J., Majda Andrew J., Concentrations in regularizations for 2-D incompressible flow, Comm. Pure Appl. Math.40 (3) (1987) 301-345. Zbl0850.76730MR882068
  3. [3] Iftimie Dragoş, Lopes Filho Milton C., Nussenzveig Lopes Helena J., Two-dimensional incompressible ideal flow around a small obstacle, Comm. Partial Differential Equations28 (1–2) (2003) 349-379. Zbl1094.76007MR1974460
  4. [4] Iftimie Dragoş, Lopes Filho Milton C., Nussenzveig Lopes Helena J., Two-dimensional incompressible viscous flow around a small obstacle, Math. Ann.336 (2) (2006) 449-489. Zbl1169.76016MR2244381
  5. [5] Iftimie Dragoş, Lopes Filho Milton C., Nussenzveig Lopes Helena J., Incompressible flow around a small obstacle and the vanishing viscosity limit, Comm. Math. Phys.289 (2009) 99-115. Zbl1173.35628MR2480743
  6. [6] Iftimie Dragoş, Kelliher James P., Remarks on the vanishing obstacle limit for a 3D viscous incompressible fluid, Proc. Amer. Math. Soc.137 (2) (2009) 685-694. Zbl1156.76018MR2448591
  7. [7] Kato Tosio, Remarks on zero viscosity limit for nonstationary Navier–Stokes flows with boundary, in: Seminar on Nonlinear Partial Differential Equations, Berkeley, CA, 1983, Math. Sci. Res. Inst. Publ., vol. 2, Springer, New York, 1984, pp. 85-98. Zbl0559.35067MR765230
  8. [8] Kelliher James P., Expanding domain limit for incompressible fluids in the plane, Comm. Math. Phys.278 (3) (2008) 753-773. Zbl1152.76017MR2373442
  9. [9] James P. Kelliher, Infinite-energy 2D statistical solutions to the equations of incompressible fluids, preprint. Zbl1179.76019MR2575367
  10. [10] Lacave Christophe, Two-dimensional incompressible ideal flow around a thin obstacle tending to a curve, Ann. Inst. H. Poincaré Anal. Non Lineaire26 (4) (2009) 1121-1148. Zbl1166.76300MR2542717
  11. [11] Christophe Lacave, Two-dimensional incompressible viscous flow around a thin obstacle tending to a curve, Proc. Royal Soc. Edinburgh: Sect. A Math., in press. Zbl1259.76007MR2557320
  12. [12] Lopes Filho Milton C., Vortex dynamics in a two-dimensional domain with holes and the small obstacle limit, SIAM J. Math. Anal.39 (2) (2007) 422-436. Zbl1286.76018MR2338413
  13. [13] Majda Andrew J., Bertozzi Andrea, Vorticity and Incompressible Flow, Cambridge Texts Appl. Math., vol. 27, Cambridge University Press, Cambridge, UK, 2002. Zbl0983.76001MR1867882
  14. [14] Temam Roger, Navier–Stokes Equations, Theory and Numerical Analysis, AMS Chelsea Publishing, Providence, RI, 2001, reprint of the 1984 edition. Zbl0981.35001MR769654

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