A note about existence for a class of viscous fluid problems

2012/03/30 by Hermenegildo Borges de Oliveira, de Oliveira, Hermenegildo Borges
Computer Science · Mathematics · #35J60 #35Q30 #35Q35 #76D03 #76D05 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1203.6799

openalex publication_date 2012/03/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this work the existence of weak solutions for a class of non-Newtonian viscous fluid problems is analyzed. The problem is modeled by the steady case of the generalized Navier-Stokes equations, where the exponent q that characterizes the flow depends on the space variable: q=q(x). For the associated boundary-value problem we show that, in some situations, the log-Hölder continuity condition on q can be dropped and the result of the existence of weak solutions still remain valid for any variable exponent q≥α>(2N)/(N+2), where α=essinf q.

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