Positive and non-positive solutions for an inviscid dyadic model: well-posedness and regularity
Positive and non-positive solutions for an inviscid dyadic model: well-posedness and regularity
复制标题
无粘二元模型的正解和非正解：适定性和正则性
DOI：
10.1007/s00030-012-0200-3
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
F. Morandin
中科院分区：
文献类型：
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作者：
D. Barbato;F. Morandin
我们改进了文献中关于无粘二元模型的正则性和唯一性结果。我们证明了对于标度系数kn = 2βn的每一个增长率β，正二矢是全局适定的。证明了正解的一些正则性结果，即a.e.t的supn $${n^{-\alpha}k_n^{\frac13}X_n(t) < \infty}$$和所有t的supn $${k_n^{\frac13-\frac1{3\beta}}X_n(t) \leq Ct^{-1/3}}$$。并且证明了在非常一般的假设下，解在有限时间后成为正的。
We improve regularity and uniqueness results from the literature for the inviscid dyadic model. We show that positive dyadic is globally well-posed for every rate of growth β of the scaling coefficients kn = 2βn. Some regularity results are proved for positive solutions, namely supn$${n^{-\alpha}k_n^{\frac13}X_n(t) < \infty}$$ for a.e. t and supn$${k_n^{\frac13-\frac1{3\beta}}X_n(t) \leq Ct^{-1/3}}$$ for all t. Moreover it is shown that under very general hypothesis, solutions become positive after a finite time.