2009/03/31 by Hermenegildo Borges de Oliveira, de Oliveira, Hermenegildo Borges · 1 citation
Earth and Planetary Sciences · Engineering · Mathematics · Physics and Astronomy · #35B40 #35Q30 #76D03 #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #FOS: Physical sciences #Geophysics and Gravity Measurements #Mathematical Physics (math-ph) #Navier-Stokes equation solutions #math-ph #math.AP #math.MP #msc:35B40 #msc:35Q30 #msc:76D03
paper · pdf · doi:10.48550/arxiv.0903.5513
22 pages
arxiv created 2009/03/31 · openalex publication_date 2009/03/31 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this work we consider the Navier-Stokes problem modified by the absorption term |u|σ-2u, where σ>1, which is introduced in the momentum equation. % For this new problem, we prove the existence of weak solutions for any dimension N≥ 2 and its uniqueness for N=2. % Then we prove that, for zero body forces, the weak solutions extinct in a finite time if 1<σ<2, exponentially decay in time if σ=2 and decay with a power-time rate if σ>2. % We prove also that for a general non-zero body forces, the weak solutions exponentially decay in time for any σ>1. In the special case of a suitable forces field which vanishes at some instant, we prove that the weak solutions extinct at the same instant provided 1<σ<2.