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

2012/01/12 by Barbato, David, Morandin, Francesco
#Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1201.2693

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) < ∞ for a.e. t and sup_n k_n^1/3-1/(3b) X_n(t) ≤ 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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