Existence and analyticity of the Lei-Lin solution of the Navier-Stokes equations on the torus

Ambrose, David; Lopes Filho, Milton; Nussenzveig Lopes, Helena

doi:10.1090/proc/16615

Existence and analyticity of the Lei-Lin solution of the Navier-Stokes equations on the torus
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by David M. Ambrose, Milton C. Lopes Filho and Helena J. Nussenzveig Lopes

Proc. Amer. Math. Soc. 152 (2024), 781-795

DOI: https://doi.org/10.1090/proc/16615

Published electronically: November 17, 2023

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Abstract:

Lei and Lin [Comm. Pure Appl. Math. 64 (2011), pp. 1297–1304] have recently given a proof of a global mild solution of the three-dimensional Navier-Stokes equations in function spaces based on the Wiener algebra. An alternative proof of existence of these solutions was then developed by Bae [Proc. Amer. Math. Soc. 143 (2015), pp. 2887–2892], and this new proof allowed for an estimate of the radius of analyticity of the solutions at positive times. We adapt the Bae proof to prove existence of the Lei-Lin solution in the spatially periodic setting, finding an improved bound for the radius of analyticity in this case.

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