Stability of bounded global solutions for Navier-Stokes equations
Oscar A. Barraza, Claudia B. Ruscitti
TL;DR
This paper investigates the long-term behavior of solutions to the Navier-Stokes equations within abstract Banach spaces, demonstrating the asymptotic stability of the zero solution under certain conditions.
Contribution
It introduces a framework for analyzing the asymptotic stability of global solutions to Navier-Stokes equations in abstract Banach spaces, extending previous stability results.
Findings
Global solutions exhibit asymptotic decay over time.
Zero solution is asymptotically stable.
Results apply to Navier-Stokes systems in abstract Banach spaces.
Abstract
In this paper some kind of asymptotic behavior of the solutions for the Navier-Stokes system on abstract Banach spaces is studied under the existence of global in time solutions. The asymptotic stability of the zero solution is also shown.
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Taxonomy
TopicsNavier-Stokes equation solutions · Advanced Mathematical Physics Problems · Stability and Controllability of Differential Equations