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Sistemas Dinâmicos

Solutions of differential equations from a non-Lipschitz singularity
Alexei A. Mailybaev

Quarta-feira, 24 de janeiro de 2018, 15:30
Sala 236.

We consider a system of ordinary differential equations with an isolated non-Lipschitz singularity. First, I will describe the motivation of using such a system as a toy-model for the phenomenon of finite-time blowup in partial differential equations describing, in particular, turbulence. Solutions passing through the non-Lipschitz singular point in finite time become strongly non-unique: there are infinite number of solutions from a singular point. So our focus will be the definition of the regularization procedure (analogous to the inviscid limit in fluid dynamics) that provides a natural selection mechanism. We will see that the selection principle reduces to the classification of attractors in a properly defined renormalized dynamical system.