Asymmetric Self-Similar Spiral Solutions of 2-D Incompressible Euler Equations

Abstract

We construct nonradial, self-similar solutions to the two-dimensional incompressible Euler equations without assuming rotational symmetry. These solutions extend the study of self-similar algebraic spiral flows, initiated by Elling and further developed by Shao–Wei–Zhang [41], where m-fold symmetry with \(m \ge 2\) was assumed. Moreover, they bear resemblance to the numerical simulations of Bressan–Shen [10], in connection with the ongoing investigation into non-uniqueness of solutions.