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The generalized Proudman-Johnson equation revisited. (English) Zbl 1270.35372
Summary: We demonstrate the existence of solutions to the inviscid generalized Proudman-Johnson equation for parameters \(a\) lying in the open interval (-5,-1) which develop singularities in finite time; moreover, we show that there are solutions which exist for all times if \(a=-1\). Finally, a simple blow-up criterion for solutions arising from a special class of initial data is given.

MSC:
35Q35 PDEs in connection with fluid mechanics
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