Thin vortex tubes in the stationary Euler equation
Alberto Enciso[1]; Daniel Peralta-Salas[1]
- [1] Instituto de Ciencias Matemáticas Consejo Superior de Investigaciones Científicas 28049 Madrid, Spain
Journées Équations aux dérivées partielles (2013)
- Volume: 192, Issue: 1, page 1-13
- ISSN: 0752-0360
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topEnciso, Alberto, and Peralta-Salas, Daniel. "Thin vortex tubes in the stationary Euler equation." Journées Équations aux dérivées partielles 192.1 (2013): 1-13. <http://eudml.org/doc/275609>.
@article{Enciso2013,
abstract = {In this paper we outline some recent results concerning the existence of steady solutions to the Euler equation in $\mathbb\{R\}^3$ with a prescribed set of (possibly knotted and linked) thin vortex tubes.},
affiliation = {Instituto de Ciencias Matemáticas Consejo Superior de Investigaciones Científicas 28049 Madrid, Spain; Instituto de Ciencias Matemáticas Consejo Superior de Investigaciones Científicas 28049 Madrid, Spain},
author = {Enciso, Alberto, Peralta-Salas, Daniel},
journal = {Journées Équations aux dérivées partielles},
keywords = {level sets; Laplace equation; global approximation; Green function},
language = {eng},
number = {1},
pages = {1-13},
publisher = {Groupement de recherche 2434 du CNRS},
title = {Thin vortex tubes in the stationary Euler equation},
url = {http://eudml.org/doc/275609},
volume = {192},
year = {2013},
}
TY - JOUR
AU - Enciso, Alberto
AU - Peralta-Salas, Daniel
TI - Thin vortex tubes in the stationary Euler equation
JO - Journées Équations aux dérivées partielles
PY - 2013
PB - Groupement de recherche 2434 du CNRS
VL - 192
IS - 1
SP - 1
EP - 13
AB - In this paper we outline some recent results concerning the existence of steady solutions to the Euler equation in $\mathbb{R}^3$ with a prescribed set of (possibly knotted and linked) thin vortex tubes.
LA - eng
KW - level sets; Laplace equation; global approximation; Green function
UR - http://eudml.org/doc/275609
ER -
References
top- V.I. Arnold, Sur la géométrie différentielle des groupes de Lie de dimension infinie et ses applications à l’hydrodynamique des fluides parfaits, Ann. Inst. Fourier 16 (1966) 319–361. Zbl0148.45301MR202082
- V.I. Arnold, B. Khesin, Topological methods in hydrodynamics, Springer, New York, 1999. Zbl0902.76001MR1612569
- D. Córdoba, C. Fefferman, On the collapse of tubes carried by 3D incompressible flows, Comm. Math. Phys. 222 (2001) 293–298. Zbl0999.76020MR1859600
- J. Deng, T.Y. Hou, X. Yu, Geometric properties and nonblowup of 3D incompressible Euler flow. Comm. PDE 30 (2005) 225–243. Zbl1142.35549MR2131052
- A. Enciso, D. Peralta-Salas, Knots and links in steady solutions of the Euler equation, Ann. of Math. 175 (2012) 345–367. Zbl1238.35092MR2874645
- A. Enciso, D. Peralta-Salas, Existence of knotted vortex tubes in steady Euler flows, arXiv:1210.6271. Zbl1317.35184
- A. Enciso, D. Peralta-Salas, Non-existence and structure for Beltrami fields with nonconstant proportionality factor, arXiv:1402.6825. Zbl06559723
- A. González-Enríquez, R. de la Llave, Analytic smoothing of geometric maps with applications to KAM theory, J. Differential Equations 245 (2008) 1243–1298. Zbl1160.37024MR2436830
- H. von Helmholtz, Über Integrale der hydrodynamischen Gleichungen, welche den Wirbelbewegungen entsprechen, J. Reine Angew. Math. 55 (1858) 25–55.
- D. Kleckner, W.T.M. Irvine, Creation and dynamics of knotted vortices, Nature Phys. 9 (2013) 253–258.
- R.B. Pelz, Symmetry and the hydrodynamic blow-up problem, J. Fluid Mech. 444 (2001) 299–320. Zbl1002.76095MR1856973
- W. Thomson (Lord Kelvin), Vortex Statics, Proc. R. Soc. Edinburgh 9 (1875) 59–73 (reprinted in: Mathematical and physical papers IV, Cambridge University Press, Cambridge, 2011, pp. 115–128).
- N. Nadirashvili, Liouville theorem for Beltrami flow, Geom. Funct. Anal. 24 (2014) 916–921. Zbl1294.35080
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