Note on the fast decay property of steady Navier–Stokes flows in the whole space
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Abstract We investigate the pointwise asymptotic behavior of solutions to the stationary Navier–Stokes equation in {\mathbb{R}^{n}} ( {n\geq 3} ). We show the existence of a unique solution {\{u,p\}} such that {|\nabla^{j}u(x)|=O(|x|^{1-n-j})} and {|\nabla^{k}p(x)|=O(|x|^{-n-k})} ( {j,k=0,1,\ldots} ) as {|x|\rightarrow\infty} , assuming the smallness of the external force and the rapid decay of its derivatives. The solution {\{u,p\}} decays more rapidly than the Stokes fundamental solution.
2012 ◽
Vol 205
(2)
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pp. 585-650
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2010 ◽
Vol 13
(1)
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pp. 1-31
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2013 ◽
Vol 45
(6)
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pp. 3514-3574
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2007 ◽
Vol 43
(3)
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pp. 763-794
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2015 ◽
Vol 219
(2)
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pp. 637-678
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