Asymptotic properties of the Stokes flow in an exterior domain with slowly decaying initial data and its application to the Navier-Stokes equations

2024/03/11 by Chang, Tongkeun, Jin, Bum Ja
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2403.07205

Abstract

In this paper, we study the decay rate of the Stokes flow in an exterior domain with a slowly decaying initial data \bf u₀(x)=O(|x|^-\al), 0<\al≤ n. %which is not L¹ integrable. As an application we find the unique strong solution of the Navier-Stokes equations corresponding to a slowly decaying initial data. We also derive the pointwise decay estimate of the Navier-Stokes flow. Our decay rates will be optimal compared with the decay rates of the heat flow.

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