Singularity tracking for Camassa-Holm and Prandtl's equations

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23 Citazioni (Scopus)

Abstract

In this paper we consider the phenomenon of singularity formation for the Camassa–Holm equation and for Prandtl’s equations. We solve these equations using spectral methods. Then we track the singularity in the complex plane estimating the rate of decay of the Fourier spectrum. This method allows us to follow the process of the singularity formation as the singularity approaches the real axis.
Lingua originaleEnglish
pagine (da-a)1108-1122
Numero di pagine15
RivistaApplied Numerical Mathematics
Volume56
Stato di pubblicazionePublished - 2006

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Camassa-Holm Equation
Singularity
Fourier Spectrum
Spectral Methods
Argand diagram

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Applied Mathematics
  • Computational Mathematics

Cita questo

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title = "Singularity tracking for Camassa-Holm and Prandtl's equations",
abstract = "In this paper we consider the phenomenon of singularity formation for the Camassa–Holm equation and for Prandtl’s equations. We solve these equations using spectral methods. Then we track the singularity in the complex plane estimating the rate of decay of the Fourier spectrum. This method allows us to follow the process of the singularity formation as the singularity approaches the real axis.",
author = "Sammartino, {Marco Maria Luigi} and Lombardo, {Maria Carmela} and Vincenzo Sciacca and Rocca, {Giulio Della}",
year = "2006",
language = "English",
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journal = "Applied Numerical Mathematics",
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AU - Sammartino, Marco Maria Luigi

AU - Lombardo, Maria Carmela

AU - Sciacca, Vincenzo

AU - Rocca, Giulio Della

PY - 2006

Y1 - 2006

N2 - In this paper we consider the phenomenon of singularity formation for the Camassa–Holm equation and for Prandtl’s equations. We solve these equations using spectral methods. Then we track the singularity in the complex plane estimating the rate of decay of the Fourier spectrum. This method allows us to follow the process of the singularity formation as the singularity approaches the real axis.

AB - In this paper we consider the phenomenon of singularity formation for the Camassa–Holm equation and for Prandtl’s equations. We solve these equations using spectral methods. Then we track the singularity in the complex plane estimating the rate of decay of the Fourier spectrum. This method allows us to follow the process of the singularity formation as the singularity approaches the real axis.

UR - http://hdl.handle.net/10447/30603

M3 - Article

VL - 56

SP - 1108

EP - 1122

JO - Applied Numerical Mathematics

JF - Applied Numerical Mathematics

SN - 0168-9274

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