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arXiv · 2610.18102

Stability Analysis of Bounded Solutions to 2-D Incompressible Navier-Stokes Equations in L^2_uloc Spaces

Haokun Tai·Xiaoxin Zheng
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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 $ν\to 0$.

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Haokun Tai, Xiaoxin Zheng. 2026-10-13. Stability Analysis of Bounded Solutions to 2-D Incompressible Navier-Stokes Equations in L^2_uloc Spaces. https://arxiv.org/abs/2610.18102

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