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arXiv · 1811.04997

Existence of regular time-periodic solution to shear-thinning fluids

Anna Abbatiello·Paolo Maremonti
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Abstract

In this note we investigate the existence of time-periodic solutions to the $p$-Navier-Stokes system in the singular case of $p\in (1, 2)$, that describes the flows of an incompressible shear-thinning fluid. In the $3D$ space-periodic setting and for $p \in [ \frac{5}{3} , 2)$ we prove the existence of a regular time-periodic solution corresponding to a time periodic force data which is assumed small in a suitable sense. As a particular case we obtain `regular' steady solutions.

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Anna Abbatiello, Paolo Maremonti. 2018-11-12. Existence of regular time-periodic solution to shear-thinning fluids. https://doi.org/10.1007/s00021-019-0435-4

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