Abstract Self-similar finite-time singularity solutions of the axisymmetric Euler equations in an infinite system with a swirl are provided. Using the Elgindi approximation of the Biot–Savart kernel for the ...

A class of constitutive relations for elastic bodies has been proposed recently, where the linearized strain tensor is expressed as a nonlinear function of the stress tensor. Considering this new type of constitutive ...

It is shown that the self-similar ansatz proposed by T. Hou and G. Luo to describe a singular solution of the 3D axisymmetric Euler equations leads, without assuming any asymptotic condition on the self-similar profiles, ...

This paper deals with the uniqueness, within a fixed topological class, of otree-likeo solutions to the evolution of networks by curve shortening flow. More precisely, we show that if for a given initial condition, there ...

We review the construction of the mixed Painlevé P III –V system in terms of a 4-boson integrable model and discuss its symmetries. Such a mixed system consist of a hybrid differential equation that for special limits of ...