## Partial regularity of the solutions to a turbulent problem in porous media

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- by H. B. de Oliveira and A. Paiva PDF
- Proc. Amer. Math. Soc.
**147**(2019), 3961-3981 Request permission

## Abstract:

A one-equation turbulent model that is being used with success in the applications to model turbulent flows through porous media is studied in this work. We consider the classical Navier–Stokes equations, with feedback forces fields, coupled with the equation for the turbulent kinetic energy (TKE) through the turbulence production term and through the turbulent and the diffusion viscosities. Under suitable growth conditions on the feedback functions involved in the model, we prove the local higher integrability of the gradient solutions to the steady version of this problem.## References

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## Additional Information

**H. B. de Oliveira**- Affiliation: FCT - Universidade do Algarve, Faro, Portugal; and CMAFCIO - Universidade de Lisboa, Portugal
- MR Author ID: 747453
- Email: holivei@ualg.pt
**A. Paiva**- Affiliation: FCT - Universidade do Algarve, Faro, Portugal
- MR Author ID: 1204242
- Received by editor(s): June 8, 2018
- Received by editor(s) in revised form: January 10, 2019
- Published electronically: June 14, 2019
- Additional Notes: The first author was partially supported by Grant SFRH/BSAB/135242/2017 and by the Project UID/MAT/04561/2013, both from the Portuguese Foundation for Science and Technology (FCT), Portugal.
- Communicated by: Catherine Sulem
- © Copyright 2019 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**147**(2019), 3961-3981 - MSC (2010): Primary 76F60, 76S05, 35J57, 35B65, 76D03
- DOI: https://doi.org/10.1090/proc/14545
- MathSciNet review: 3993789