Global and singular solutions to the generalized Proudman–Johnson equation

Abstract

We show that there is a class of solutions to the generalized Proudman–Johnson equation which exist globally for all parameters a having the form − n + 3 n + 1 for n ∈ N , thereby extending a result of Bressan and Constantin (2005) [2]. Furthermore, we present new proofs of existence of solutions developing spontaneous singularities and compute the corresponding blow-up rates.