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arXiv · 2410.11796

Spatial decay/asymptotics in the Navier-Stokes equation

Peter Topalov
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Abstract

We discuss the appearance of spatial asymptotic expansions of solutions of the Navier-Stokes equation on $\mathbb{R}^n$. In particular, we prove that the Navier-Stokes equation is locally well-posed in a class of weighted Sobolev and asymptotic spaces. The solutions depend analytically on the initial data and time and (generically) develop non-trivial asymptotic terms as $|x|\to\infty$. In addition, the solutions have a spatial smoothing property that depends on the order of the asymptotic expansion.

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Peter Topalov. 2024-10-15. Spatial decay/asymptotics in the Navier-Stokes equation. https://arxiv.org/abs/2410.11796

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