Singularity tracking for Camassa–Holm and Prandtlʹs equations Original Research Article

In this paper we consider the phenomenon of singularity formation for the Camassa–Holm equation and for Prandtlʹs 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.