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-αkn1/3Xn(t) < ∞ for a.e. t and supnkn1/3-1/3βXn(t) ≤ Ct-1/3 for all t. Moreover it is shown that under very general hypothesis, solutions become positive after a finite time. © 2012 Springer Basel AG.
Positive and non-positive solutions for an inviscid dyadic model: Well-posedness and regularity
Barbato D.;Morandin F.
2013-01-01
Abstract
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-αkn1/3Xn(t) < ∞ for a.e. t and supnkn1/3-1/3βXn(t) ≤ Ct-1/3 for all t. Moreover it is shown that under very general hypothesis, solutions become positive after a finite time. © 2012 Springer Basel AG.File in questo prodotto:
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