On the stationary solutions and inviscid limit for the generalized Proudman–Johnson equation with O(1) forcing

초록

We consider the stationary problem for the generalized Proudman–Johnson equation ψψxxx−aψxψxx=νψxxxx+f, where a∈R and ν>0 are parameters and ψ and f satisfy the periodic boundary conditions on [−π,π]. We establish the existence of a time-dependent solution and the uniqueness of the stationary solution for some large ν. Then, we investigate the behavior of solution sequences in the limit ν→0+, fixing a and f, where bifurcations appear and new solutions emerge. In particular, we analyze if there is convergence towards stationary solutions for the corresponding inviscid equation. © 2018 Elsevier Inc.

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