Corpus ID: 220546235

Non Uniqueness of power-law flows

@article{Burczak2020NonUO,
  title={Non Uniqueness of power-law flows},
  author={Jan Burczak and Stefano Modena and L. Sz{\'e}kelyhidi},
  journal={arXiv: Analysis of PDEs},
  year={2020}
}

Jan Burczak, Stefano Modena, L. Székelyhidi

Published 2020

Mathematics

arXiv: Analysis of PDEs

We apply the technique of convex integration to obtain non-uniqueness and existence results for power-law fluids, in dimension $d\ge 2$. For the power index $q$ below the compactness threshold, i.e. $q \in (1, \frac{2d}{d+2})$, we show ill-posedness of Leray-Hopf solutions. For a wider class of indices $q \in (1, \frac{3d+2}{d+2})$ we show ill-posedness of distributional (non-Leray-Hopf) solutions, extending the seminal paper of Buckmaster and Vicol. In this wider class we also construct non… CONTINUE READING

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