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arXiv · 2210.04836

Spatial asymptotic expansions in the Navier-Stokes equation

R. McOwen·P. Topalov
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Abstract

We prove that the Navier-Stokes equation for a viscous incompressible fluid in $\mathbb{R}^d$ is locally well-posed in spaces of functions allowing spatial asymptotic expansions with log terms as $|x|\to\infty$ of any a priori given order. The solution depends analytically on the initial data and time so that for any $0<\vartheta<\pi/2$ it can be holomorphically extended in time to a conic sector in $\mathbb{C}$ with angle $2\vartheta$ at zero. We discuss the approximation of solutions by their asymptotic parts.

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R. McOwen, P. Topalov. 2022-10-10. Spatial asymptotic expansions in the Navier-Stokes equation. https://arxiv.org/abs/2210.04836

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