Adiabatic Approximation for the Motion of Ginzburg-Landau Vortex Filaments

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Adiabatic Approximation for the Motion of Ginzburg-Landau Vortex Filaments. / Zhang, Jingxuan.

In: Communications in Mathematical Physics, Vol. 389, 2022, p. 1061–1085.

Research output: Contribution to journal › Journal article › Research › peer-review

Harvard

Zhang, J 2022, 'Adiabatic Approximation for the Motion of Ginzburg-Landau Vortex Filaments', Communications in Mathematical Physics, vol. 389, pp. 1061–1085. https://doi.org/10.1007/s00220-021-04258-w

APA

Zhang, J. (2022). Adiabatic Approximation for the Motion of Ginzburg-Landau Vortex Filaments. Communications in Mathematical Physics, 389, 1061–1085. https://doi.org/10.1007/s00220-021-04258-w

Vancouver

Zhang J. Adiabatic Approximation for the Motion of Ginzburg-Landau Vortex Filaments. Communications in Mathematical Physics. 2022;389:1061–1085. https://doi.org/10.1007/s00220-021-04258-w

Author

Zhang, Jingxuan. / Adiabatic Approximation for the Motion of Ginzburg-Landau Vortex Filaments. In: Communications in Mathematical Physics. 2022 ; Vol. 389. pp. 1061–1085.

Bibtex

@article{a7df20edb5c045718dbdc23055fbacb5,
title = "Adiabatic Approximation for the Motion of Ginzburg-Landau Vortex Filaments",
abstract = "In this paper, we consider the concentration property of solutions to the dispersive Ginzburg-Landau (or Gross-Pitaevskii) equation in three dimensions. On a spatial domain, it has long been conjectured that such a solution concentrates near some curve evolving according to the binormal curvature flow, and conversely, that a curve moving this way can be realized in a suitable sense by some solution to the dispersive Ginzburg-Landau equation. Some partial results are known with rather strong symmetry assumptions. Our main theorems here provide affirmative answer to both conjectures under certain small curvature assumption. The results are valid for small but fixed material parameter in the equation, in contrast to the general practice to take this parameter to its zero limit. The advantage is that we can retain precise description of the vortex filament structure. The results hold on a long but finite time interval, depending on the curvature assumption.",
author = "Jingxuan Zhang",
year = "2022",
doi = "10.1007/s00220-021-04258-w",
language = "English",
volume = "389",
pages = "1061–1085",
journal = "Communications in Mathematical Physics",
issn = "0010-3616",
publisher = "Springer",

}

RIS

TY - JOUR

T1 - Adiabatic Approximation for the Motion of Ginzburg-Landau Vortex Filaments

AU - Zhang, Jingxuan

PY - 2022

Y1 - 2022

N2 - In this paper, we consider the concentration property of solutions to the dispersive Ginzburg-Landau (or Gross-Pitaevskii) equation in three dimensions. On a spatial domain, it has long been conjectured that such a solution concentrates near some curve evolving according to the binormal curvature flow, and conversely, that a curve moving this way can be realized in a suitable sense by some solution to the dispersive Ginzburg-Landau equation. Some partial results are known with rather strong symmetry assumptions. Our main theorems here provide affirmative answer to both conjectures under certain small curvature assumption. The results are valid for small but fixed material parameter in the equation, in contrast to the general practice to take this parameter to its zero limit. The advantage is that we can retain precise description of the vortex filament structure. The results hold on a long but finite time interval, depending on the curvature assumption.

AB - In this paper, we consider the concentration property of solutions to the dispersive Ginzburg-Landau (or Gross-Pitaevskii) equation in three dimensions. On a spatial domain, it has long been conjectured that such a solution concentrates near some curve evolving according to the binormal curvature flow, and conversely, that a curve moving this way can be realized in a suitable sense by some solution to the dispersive Ginzburg-Landau equation. Some partial results are known with rather strong symmetry assumptions. Our main theorems here provide affirmative answer to both conjectures under certain small curvature assumption. The results are valid for small but fixed material parameter in the equation, in contrast to the general practice to take this parameter to its zero limit. The advantage is that we can retain precise description of the vortex filament structure. The results hold on a long but finite time interval, depending on the curvature assumption.

UR - http://www.scopus.com/inward/record.url?scp=85119160032&partnerID=8YFLogxK

U2 - 10.1007/s00220-021-04258-w

DO - 10.1007/s00220-021-04258-w

M3 - Journal article

AN - SCOPUS:85119160032

VL - 389

SP - 1061

EP - 1085

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

ER -

ID: 289461717