Blow-up rate of solution to generalised Blasius equation

TL;DR

This paper determines the blow-up rate of solutions to a generalized Blasius equation by analyzing the long-term behavior of a related Lotka-Volterra system, connecting fluid dynamics and probabilistic models.

Contribution

It introduces a novel approach linking blow-up rates of differential equations to the dynamics of a Lotka-Volterra system, providing new insights into the generalized Blasius equation.

Findings

Identified the blow-up rate of solutions to the generalized Blasius equation.

Connected the blow-up behavior to the long-time dynamics of a Lotka-Volterra system.

Enhanced understanding of the mathematical properties of the generalized Blasius equation.

Abstract

We identify the blow-up rate of a solution to a generalised Blasius equation, that we came across while studying a probabilistic model of "Poissonian burning" in Euclidean space. Our proof involves the study of the long-time behaviour of solutions to a Lotka--Volterra system.