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On the existence of weak solutions to a stationary one-equation RANS model with unbounded eddy viscosities

Abstract

We study a one-equation RANS model with eddy viscosities that include, as a special case, the classical Kolmogorov–Prandtl expression. Under mild assumptions on the data, we prove the existence of a weak solution involving a defect measure. For external forces with sufficiently small norm, we obtain the existence of a weak solution in the usual sense.

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Correspondence to Pierre-Étienne Druet.

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Druet, PÉ., Naumann, J. On the existence of weak solutions to a stationary one-equation RANS model with unbounded eddy viscosities. Ann. Univ. Ferrara 55, 67–87 (2009). https://doi.org/10.1007/s11565-009-0062-8

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Keywords

  • Navier–Stokes equations
  • Turbulent kinetic energy
  • Kolmogorov–Prandtl expression
  • Meyers’ estimate

Mathematics Subject Classification (2000)

  • 76D03
  • 76D05
  • 76F05
  • 35J99