Positive and non-positive solutions for an inviscid dyadic model: well-posedness and regularity

Autor:	Francesco Morandin, David Barbato
Rok vydání:	2012
Předmět:	Applied Mathematics Combinatorics Mathematics - Analysis of PDEs Mathematics - Classical Analysis and ODEs Inviscid flow Classical Analysis and ODEs (math.CA) FOS: Mathematics Uniqueness Finite time Scaling Analysis Well posedness Analysis of PDEs (math.AP) Mathematics Rate of growth
Zdroj:	Nonlinear Differential Equations and Applications NoDEA. 20:1105-1123
ISSN:	1420-9004 1021-9722
DOI:	10.1007/s00030-012-0200-3
Popis:	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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::260138a14b39932f938dfecc40622a31 https://doi.org/10.1007/s00030-012-0200-3 Zobrazit plný text záznamu Full text from SpringerLink