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

@article{Barbato2012PositiveAN,
  title={Positive and non-positive solutions for an inviscid dyadic model: well-posedness and regularity},
  author={David G. Barbato and Francesco Morandin},
  journal={Nonlinear Differential Equations and Applications NoDEA},
  year={2012},
  volume={20},
  pages={1105-1123}
}
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… CONTINUE READING

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