Formal asymptotics of bubbling in the harmonic map heat flow

G.J.B. van den Berg; J. Hulshof; J.R. King

doi:10.1137/S0036139902408874

Formal asymptotics of bubbling in the harmonic map heat flow

G.J.B. van den Berg, J. Hulshof, J.R. King

Mathematics

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Abstract

The harmonic map heat flow is a model for nematic liquid crystals and also has origins in geometry. We present an analysis of the asymptotic behavior of singularities arising in this flow for a special class of solutions which generalizes a known (radially symmetric) reduction. Specifically, the rate at which blowup occurs is investigated in settings with certain symmetries, using the method of matched asymptotic expansions. We identify a range of blowup scenarios in both finite and infinite time, including degenerate cases.

Original language	English
Pages (from-to)	1682-1717 (electronic)
Journal	SIAM journal on applied mathematics
Volume	63
Issue number	5
DOIs	https://doi.org/10.1137/S0036139902408874
Publication status	Published - 2003

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MR2001215

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abstract = "The harmonic map heat flow is a model for nematic liquid crystals and also has origins in geometry. We present an analysis of the asymptotic behavior of singularities arising in this flow for a special class of solutions which generalizes a known (radially symmetric) reduction. Specifically, the rate at which blowup occurs is investigated in settings with certain symmetries, using the method of matched asymptotic expansions. We identify a range of blowup scenarios in both finite and infinite time, including degenerate cases.",

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AU - Hulshof, J.

AU - King, J.R.

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N2 - The harmonic map heat flow is a model for nematic liquid crystals and also has origins in geometry. We present an analysis of the asymptotic behavior of singularities arising in this flow for a special class of solutions which generalizes a known (radially symmetric) reduction. Specifically, the rate at which blowup occurs is investigated in settings with certain symmetries, using the method of matched asymptotic expansions. We identify a range of blowup scenarios in both finite and infinite time, including degenerate cases.

AB - The harmonic map heat flow is a model for nematic liquid crystals and also has origins in geometry. We present an analysis of the asymptotic behavior of singularities arising in this flow for a special class of solutions which generalizes a known (radially symmetric) reduction. Specifically, the rate at which blowup occurs is investigated in settings with certain symmetries, using the method of matched asymptotic expansions. We identify a range of blowup scenarios in both finite and infinite time, including degenerate cases.

U2 - 10.1137/S0036139902408874

DO - 10.1137/S0036139902408874

M3 - Article

VL - 63

SP - 1682-1717 (electronic)

JO - SIAM journal on applied mathematics

JF - SIAM journal on applied mathematics

SN - 0036-1399

IS - 5

ER -

Formal asymptotics of bubbling in the harmonic map heat flow

Abstract

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