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Asymptotics of Stationary Navier Stokes Equations in Higher Dimensions

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Abstract

We show that the asymptotics of solutions to stationary Navier Stokes equations in 4, 5 or 6 dimensions in the whole space with a smooth compactly supported forcing are given by the linear Stokes equation. We do not need to assume any smallness condition. The result is in contrast to three dimensions, where the asymptotics for steady states are different from the linear Stokes equation, even for small data, while the large data case presents an open problem. The case of dimension n = 2 is still harder.

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  1. Department of Mathematics, University of Minnesota, 206 Church St S. E., Minneapolis, MN, 55455, USA

    Hao Jia & Vladimír Šverák

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  1. Hao Jia
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  2. Vladimír Šverák
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Correspondence to Hao Jia.

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Jia, H., Šverák, V. Asymptotics of Stationary Navier Stokes Equations in Higher Dimensions. Acta. Math. Sin.-English Ser. 34, 598–611 (2018). https://doi.org/10.1007/s10114-017-7397-3

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