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Amplitude Blowup without Shock Formation in Compressible Euler flow

PDE and Applied Math Seminar

Speaker: Kris Jenssen, Penn St.
Location: Zoom
Start time: Thu, Jan 23 2025, 4:10PM

Recent works have demonstrated, with varying degrees of rigor, that continuously imploding self-similar radial Euler flows can drive primary (non-differentiated) flow variables to infinity at the center of motion. Among the variables that blow up is the pressure, and it is unsurprising that this can result in an outgoing shock wave in the ensuing flow.

After describing these solutions we outline a recently established, alternative scenario where a continuous 3-d flow suffers blowup, including in pressure,and yet remains continuous beyond collapse. Time permitting we will remark on the original motivation for this work, viz. to what extent such solutions can yield examples of non-unique continuation.