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arXiv · 1811.03249

Global Navier-Stokes flows for non-decaying initial data with slowly decaying oscillation

Hyunju Kwon·Tai-Peng Tsai
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Abstract

Consider the Cauchy problem of incompressible Navier-Stokes equations in $\mathbb{R}^3$ with uniformly locally square integrable initial data. If the square integral of the initial datum on a ball vanishes as the ball goes to infinity, the existence of a time-global weak solution has been known. However, such data do not include constants, and the only known global solutions for non-decaying data are either for perturbations of constants, or when the velocity gradients are in $L^p$ with finite $p$. In this paper, we construct global weak solutions for non-decaying initial data whose local oscillations decay, no matter how slowly.

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Hyunju Kwon, Tai-Peng Tsai. 2018-11-08. Global Navier-Stokes flows for non-decaying initial data with slowly decaying oscillation. https://arxiv.org/abs/1811.03249

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