Blow-up of Solutions to the Generalized Inviscid Proudman–Johnson Equation

For arbitrary values of a parameter \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\lambda \in \mathbb{R},}$$\end{document} finite-time blow-up of solutions to the generalized, inviscid Proudman–Johnson equation is studied via a direct approach which involves the derivation of representation formulae for solutions to the problem.