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

Abstract

For arbitrary values of a parameter $\lambda \in R$, 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.

33 pages. Accepted for publication in Journal of Mathematical Fluid Mechanics

Cited by in corpus (3)

• A geometric view on the generalized Proudman-Johnson and $r$-Hunter-Saxton equations
• The $L^p$-Fisher-Rao metric and Amari-Cencov $\alpha$-connections
• Finite-time blowup for the inviscid vortex stretching equation