Spatial asymptotic expansions in the Navier-Stokes equation

2022/10/10 by R. McOwen, McOwen, R., P. Topalov +1
Chemical Engineering · Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Rheology and Fluid Dynamics Studies

paper · pdf · doi:10.48550/arxiv.2210.04836

openalex publication_date 2022/10/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

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