2011/09/23 by Hermenegildo Borges de Oliveira, de Oliveira, Hermenegildo Borges
Engineering · Mathematics · #35D05 #35K55 #35Q30 #76D03 #76D05 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations #math.AP #msc:35D05 #msc:35K55 #msc:35Q30 #msc:76D03 #msc:76D05
paper · pdf · doi:10.48550/arxiv.1109.5217
24 pages, http://arxiv.org/submit/0324386/pdf
openalex publication_date 2011/09/23 · arxiv created 2011/09/24 · arxiv updated 2011/09/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this work we consider the generalized Navier-Stoke equations with the presence of a damping term in the momentum equation. % The problem studied here derives from the set of equations which govern the isothermal flow of incompressible, homogeneous and non-Newtonian fluids. % For the generalized Navier-Stokes problem with damping, we prove the existence of weak solutions by using regularization techniques, the theory of monotone operators and compactness arguments together with the local decomposition of the pressure and the Lipschitz-truncation method. The existence result proved here holds for any q>(2N)/(N+2) and any σ>1, where q is the exponent of the diffusion term and σ is the exponent which characterizes the damping term.