On the Slightly Perturbed De Gregorio Model on $$S^1$$
On the Slightly Perturbed De Gregorio Model on $$S^1$$
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DOI：
10.1007/s00205-021-01685-w
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发表时间：
2020-10
影响因子：
2.5
通讯作者：
Jiajie Chen
中科院分区：
文献类型：
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作者：
Jiajie Chen
本文证明了由Okamoto，Sakajo和Wunsch推广的Constantin-Lax-Majda模型（gCLM）可以从光滑的初始数据发展出有限时间奇异性。对于端点情形，当a接近且小于1时，我们证明了圆上gCLM的有限时间渐近自相似爆破。对于具有相同初始值的圆上的gCLM，若平流强度略大于1，我们证明了解的整体存在性，并且在很长时间内以衰减率衰减。两种不同行为之间的转换阈值为，这对应于De Gregorio模型。
It is conjectured that the generalization of the Constantin–Lax–Majda model (gCLM), due to Okamoto, Sakajo and Wunsch, can develop a finite time singularity from smooth initial data for. For the endpoint case whereais close to and less than 1, we prove finite time asymptotically self-similar blowup of gCLM on a circle from a class of smooth initial data. For the gCLM on a circle with the same initial data, if the strength of advectionais slightly larger than 1, we prove that the solution exists globally withdecaying in a rate offor large time. The transition threshold between two different behaviors is, which corresponds to the De Gregorio model.