Existence and isoperimetric characterization of steady spherical vortex rings in a uniform flow in R-N

G R Burton, L Preciso

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3 Citations (Scopus)

Abstract

We study a boundary-value problem for a particular semilinear elliptic equation on R-n (n greater than or equal to 2), whose solutions represent generalized stream functions for steady axisymmetric ideal fluid flows. Solutions are shown to exist that generalize those already known in dimensions 2 and 3. An isoperimetric characterization is given for our solutions, which represent generalized spherical vortex-rings. As a corollary, a sharp Sobolev-type inequality is obtained.
Original languageEnglish
Pages (from-to)449-476
Number of pages28
JournalProceedings of the Royal Society of Edinburgh Section A - Mathematics
Volume134
Publication statusPublished - 2004

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Vortex Ring
Isoperimetric
Ideal Fluid
Semilinear Elliptic Equations
Stream Function
Generalized Functions
Fluid Flow
Corollary
Boundary Value Problem
Generalise

Cite this

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title = "Existence and isoperimetric characterization of steady spherical vortex rings in a uniform flow in R-N",
abstract = "We study a boundary-value problem for a particular semilinear elliptic equation on R-n (n greater than or equal to 2), whose solutions represent generalized stream functions for steady axisymmetric ideal fluid flows. Solutions are shown to exist that generalize those already known in dimensions 2 and 3. An isoperimetric characterization is given for our solutions, which represent generalized spherical vortex-rings. As a corollary, a sharp Sobolev-type inequality is obtained.",
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T1 - Existence and isoperimetric characterization of steady spherical vortex rings in a uniform flow in R-N

AU - Burton, G R

AU - Preciso, L

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PY - 2004

Y1 - 2004

N2 - We study a boundary-value problem for a particular semilinear elliptic equation on R-n (n greater than or equal to 2), whose solutions represent generalized stream functions for steady axisymmetric ideal fluid flows. Solutions are shown to exist that generalize those already known in dimensions 2 and 3. An isoperimetric characterization is given for our solutions, which represent generalized spherical vortex-rings. As a corollary, a sharp Sobolev-type inequality is obtained.

AB - We study a boundary-value problem for a particular semilinear elliptic equation on R-n (n greater than or equal to 2), whose solutions represent generalized stream functions for steady axisymmetric ideal fluid flows. Solutions are shown to exist that generalize those already known in dimensions 2 and 3. An isoperimetric characterization is given for our solutions, which represent generalized spherical vortex-rings. As a corollary, a sharp Sobolev-type inequality is obtained.

M3 - Article

VL - 134

SP - 449

EP - 476

JO - Proceedings of the Royal Society of Edinburgh Section A - Mathematics

JF - Proceedings of the Royal Society of Edinburgh Section A - Mathematics

SN - 0308-2105

ER -