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.
DELLA ROCCA G, LOMBARDO MC, SAMMARTINO M, SCIACCA V (2006). Singularity tracking for Camassa-Holm and Prandtl's equations. APPLIED NUMERICAL MATHEMATICS, 56(8), 1108-1122 [10.1016/j.apnum.2005.09.009].
Singularity tracking for Camassa-Holm and Prandtl's equations
LOMBARDO, Maria Carmela;SAMMARTINO, Marco Maria Luigi;SCIACCA, Vincenzo
2006-01-01
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.
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