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arXiv · 2409.12918

Asymptotic stability for the 3D Navier-Stokes equations in $L^3$ and nearby spaces

Zachary Bradshaw·Weinan Wang
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Abstract

We provide a short proof of $L^3$-asymptotic stability around vector fields that are small in weak-$L^3$, including small Landau solutions. We show that asymptotic stability also holds for vector fields in the range of Lorentz spaces strictly between $L^3$ and weak-$L^3$, as well as in the closure of the test functions in weak-$L^3$. To provide a comprehensive perspective on the matter, we observe that asymptotic stability of Landau solutions does not generally extend to weak-$L^3$ via a counterexample.

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Zachary Bradshaw, Weinan Wang. 2024-09-19. Asymptotic stability for the 3D Navier-Stokes equations in $L^3$ and nearby spaces. https://arxiv.org/abs/2409.12918

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