Nonlinear Darcy Laws for Generalized Newtonian Fluids with Orlicz Growth and Oscillating Navier Slip in Periodic Porous Media
Abstract
We study the periodic homogenization of a stationary generalized Navier--Stokes system in a periodically perforated domain Ω⊂ℝN, N∈{2,3}, with a heterogeneous bulk stress of general Orlicz growth and an oscillating nonlinear Navier friction law on the pore walls, both at the Darcy scale. If the lower growth exponent at infinity satisfies p-∞>3N/(N+2) and the inertial exponent exceeds κc:=1+N(2/p-∞−1)+, inertia vanishes and, under strict monotonicity of the bulk stress, the whole family converges to the nonlinear Darcy law U=𝒦(f−∇ p0), divU=0, U·ν=0. The permeability map 𝒦 is continuous, strictly monotone, obeys two-sided Orlicz bounds and incorporates the wall slip through a nonlinear cell problem, and the extended microscopic pressure converges strongly to p0. The proof relies on a uniform Orlicz--Korn inequality, a Darcy-scaled two-scale trace theorem and a coupled bulk--surface Minty argument.
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BibTeX
@misc{douanla2026nonlinear,
title = {{Nonlinear Darcy Laws for Generalized Newtonian Fluids with Orlicz Growth and Oscillating Navier Slip in Periodic Porous Media}},
author = {Hermann Douanla and Joel Fotso Tachago and Jean Louis Woukeng},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.04587},
eprint = {2611.04587},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.04587},
}
RIS
TY - UNPB
TI - Nonlinear Darcy Laws for Generalized Newtonian Fluids with Orlicz Growth and Oscillating Navier Slip in Periodic Porous Media
AU - Hermann Douanla
AU - Joel Fotso Tachago
AU - Jean Louis Woukeng
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.04587
UR - https://arxiv.org/abs/2611.04587
AB - We study the periodic homogenization of a stationary generalized Navier--Stokes system in a periodically perforated domain Ω⊂ℝ^N, N∈{2,3}, with a heterogeneous bulk stress of general Orlicz growth and an oscillating nonlinear Navier friction law on the pore walls, both at the Darcy scale. If the lower growth exponent at infinity satisfies p^-_∞>3N/(N+2) and the inertial exponent exceeds κ_c:=1+N(2/p^-_∞−1)_+, inertia vanishes and, under strict monotonicity of the bulk stress, the whole family converges to the nonlinear Darcy law U=𝒦(f−∇ p_0), divU=0, U·ν=0. The permeability map 𝒦 is continuous, strictly monotone, obeys two-sided Orlicz bounds and incorporates the wall slip through a nonlinear cell problem, and the extended microscopic pressure converges strongly to p_0. The proof relies on a uniform Orlicz--Korn inequality, a Darcy-scaled two-scale trace theorem and a coupled bulk--surface Minty argument.
ER -