A Semi-Analytic Approach to Euler Singularities

A Semi-analytic Approach to Euler Singularities

This paper reviews the efforts to construct (or prove the impossibility of) singular solutions of the Euler equations for three dimensional incompressible flow. A semi-analytic approach to this problem is formulated based on numerical computation of complex traveling wave solutions, followed by perturbation construction of a real solution, for axisymmetric flow with swirl. The perturbation anal...

Fast semi-analytic computation of elastic edge singularities

The singularities that we consider are the characteristic non-smooth solutions of the equations of linear elasticity in piecewise homogeneous media near two dimensional corners or three dimensional edges. We describe here a method to compute their singularity exponents and the associated angular singular functions. We present the implementation of this method in a program whose input data are g...

A Semi Analytic Approach to the Robust Stability of Quasipolynomials

A semi-analytic tool for the study of the robust stability of time delay systems is presented. The approach is based on graphical methods. The conditions of the Finite Nyquist Theorem for quasipolynomials given in (Santos et al., 2003b) are improved. The Finite Inclusions Theorem for polytopic and interval quasipolynomials families is derived. An algorithm describing how to apply this new techn...

Finite-time Euler singularities: A Lagrangian perspective

Microlocal Analytic Singularities

These notes approximately represent the contents of a course given at l’Université de Paris Sud in Spring 1981 and in an accelerated version at Lund University. They are based on about three years of work with analytic singularities. The author arrived at this subject through the study of the propagation of analytic singularities for boundary value problems. Among the three existing definitions...