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Title:
On self-similar singular solutions of the De Gregorio model
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Abstract:
The De Gregorio model was suggested in the 1990s by Salvatore De Gregorio as a modification of the well-known Constantin-Lax-Majda model. The modification involves adding an advection term, making the structure of the equation closer to the Euler equations. Similarly to the Constantin-Lax-Majda model, the De Gregorio model can play an important role in testing new ideas. The existence of self-similar singular solutions of the De Gregorio model on the real line was established a few years ago via a computer-assisted proof by Chen, Hou, and Huang. I will discuss recent joint work with Hao Jia on the existence of additional self-similar solutions. It turns out that the Chen-Hou-Huang solution is the first member of a countable family. The solutions have connections to other classical topics.
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