Abstract:
We describe an approach for the construction of
singular solutions to the 3D Euler equations for
complex initial data. The approach is based on a
numerical simulation of complex traveling wave
solutions with imaginary wave speed, originally
developed by Caflisch for axisymmetric flow with
swirl. Here, we simplify and generalize this
construction to calculate traveling wave solutions
in a fully 3D (nonaxisymmetric) geometry. We also
discuss a semianalytic approach to the problem of
Euler singularities based on numerical computation
of the complex traveling wave solutions, followed by
perturbation construction of a real solution. The
perturbation analysis depends on a small amplitude
of the singularity in the traveling wave solution;
techniques for producing such a small amplitude are
described. This is joint work with Russel Caflisch.
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