Stability Analysis of Bounded Solutions to 2-D Incompressible Navier-Stokes Equations in L^2_uloc Spaces
Year: 2026
Type: preprint
Abstract: This paper examines the stability analysis of two-dimensional incompressible fluids in $L^2_{uloc}$ spaces. Extending the classical stability framework for Euler equations in Yudovich-type settings, we establish the convergence of Navier-Stokes solutions toward Euler solutions as viscosity $ν\to 0$, under the weakened assumptions $u^ν_0 \in L^\infty$ and $ω^ν_0 \in L^\infty$ without imposing decay conditions at infinity. We first derive a priori estimates for the Navier-Stokes equations in $L^\infty$ spaces. Then, using harmonic analysis tools including Littlewood-Paley decomposition and Bony's paraproduct calculus, we prove the $L^\infty$-convergence of the velocity field and $L^2_{uloc}$-convergence of the vorticity as $ν\to 0$.
Source: arXiv (Cornell University)
Authors: Tai, Haokun, Zheng, Xiaoxin
Institution: Beihang University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G7831469969
OpenAlex ID: W7221788694