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arXiv · 1201.2693

Positive and non-positive solutions for an inviscid dyadic model. Well-posedness and regularity

David Barbato·Francesco Morandin
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Abstract

We improve regolarity 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 k_n = 2^{bn}. Some regularity results are proved for positive solutions, namely \sup_n n^{-a} k_n^{1/3} X_n(t) < \infty for a.e. t and \sup_n k_n^{1/3-1/(3b)} X_n(t) \leq C t^{-1/3}$ for all $t$. Moreover it is shown that under very general hypothesis, solutions become positive after a finite time.

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David Barbato, Francesco Morandin. 2012-01-12. Positive and non-positive solutions for an inviscid dyadic model. Well-posedness and regularity. https://arxiv.org/abs/1201.2693

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