# On the Finite Time Blowup of the De Gregorio Model for the 3D Euler Equations

@article{Chen2019OnTF, title={On the Finite Time Blowup of the De Gregorio Model for the 3D Euler Equations}, author={Jiajie Chen and Thomas Y. Hou and De Huang}, journal={Communications on Pure and Applied Mathematics}, year={2019}, volume={74} }

We present a novel method of analysis and prove finite time asymptotically self‐similar blowup of the De Gregorio model [13, 14] for some smooth initial data on the real line with compact support. We also prove self‐similar blowup results for the generalized De Gregorio model [41] for the entire range of parameter on ℝ or S1 for Hölder‐continuous initial data with compact support. Our strategy is to reformulate the problem of proving finite time asymptotically self‐similar singularity into the…

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The well-known Constantin–Lax–Majda (CLM) equation, an important toy model of the 3D Euler equations without convection, can develop finite time singularities (Constantin et al. in Commun Pure Appl…

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