Evidence of a finite-time pointlike singularity solution for the Euler equations for perfect fluids

To find a blow-up solution to the Euler equations in an infinite domain is related to the zero viscosity limit of the Clay Institute's sixth Millennium Problem. Evidence of a point-like, self-similar, blow-up solution occurring in an axisymmetric flow with infinite domain is provided by solving a nonlinear eigenvalue problem for a self-similar velocity with an unknown exponent. An angular expansion is used to map the problem into an infinite hierarchy of ODEs, which shows a convergent scenario of solutions for different truncations. This approach suggests an exponent of approximately 2. This solution contrasts with the previously found annular blow-up at a cylindrical domain boundary, which exhibited an exponent of 2.91.