Existence of Regular Time-Periodic Solutions to Shear-Thinning Fluids

  • Anna Abbatiello
  • Paolo MaremontiEmail author


In this note we investigate the existence of time-periodic solutions to the p-Navier–Stokes system in the singular case of \(p\in (1,2)\), which 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 datum that is assumed small in a suitable sense. As a particular case we obtain “regular” steady solutions.


p-Navier-Stokes problem Time-periodic solutions Global existence 

Mathematics Subject Classification

35Q35 35B10 76A05. 


Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflicts of interest.


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Authors and Affiliations

  1. 1.Dipartimento di Matematica e FisicaUniversità degli Studi della Campania “Luigi Vanvitelli”CasertaItaly

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