A Borel transform method for locating singularities of Taylor and Fourier series

DOI10.1007/s10955-007-9307-zzbMath1126.44001arXivnlin/0609025OpenAlexW1993628424MaRDI QIDQ2641375

Walter Pauls, Uriel Frisch

Publication date: 20 August 2007

Published in: Journal of Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/nlin/0609025

zbMATH Keywords

nonlinear dynamicsBurgers equationcomplex singularitiesinterpolation methodBorel-Laplace transformasymptotic interpolationseries analysis

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Transform methods (e.g., integral transforms) applied to PDEs (35A22) Laplace transform (44A10)

Related Items (13)

Complex singularities in KdV solutions ⋮ Analytic structure of solutions of the one-dimensional Burgers equation with modified dissipation ⋮ Regularized Euler-\(\alpha \) motion of an infinite array of vortex sheets ⋮ Entire solutions of hydrodynamical equations with exponential dissipation ⋮ Dynamics of Complex Singularities of Nonlinear PDEs ⋮ A constructive approach to regularity of Lagrangian trajectories for incompressible Euler flow in a bounded domain ⋮ Extended self-similarity works for the Burgers equation and why ⋮ On complex singularities of the 2D Euler equation at short times ⋮ The Cauchy-Lagrangian method for numerical analysis of Euler flow ⋮ On asymptotic extrapolation ⋮ Singularity formation for Prandtl's equations ⋮ Analysis of complex singularities in high-Reynolds-number Navier–Stokes solutions ⋮ Complex singularity analysis for vortex layer flows

Cites Work

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• Extrapolation methods theory and practice
• Singularities of Euler flow? Not out of the blue!
• Relax, but don't be too lazy
• Convergence acceleration of Taylor sections by convolution
• Transseries and real differential algebra
• On effective analytic continuation
• Nature of complex singularities for the 2D Euler equation
• Small-scale structure of the Taylor–Green vortex
• Deducing the Properties of Singularities of Functions from their Taylor Series Coefficients
• Analytic structure of vortex sheet dynamics. Part 1. Kelvin–Helmholtz instability
• A study of singularity formation in vortex-sheet motion by a spectrally accurate vortex method
• The spontaneous appearance of a singularity in the shape of an evolving vortex sheet
• Self-avoiding polygons on the square lattice
• The Rational Approximation of Functions which are Formally Defined by a Power Series Expansion

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