Abstract
In the exterior domain Ω⊂ℝ2 we consider the two-dimensional Navier-stokes system Δu-▽p=(u,▽)u, div u=0 whose solution possesses a finite Dirichlet integral and satisfies the condition lim|x|→∞ u(x)=(1, 0). For this solution, we establish the estimate |u(x)−(1, 0)|≤c|x| −α, where α>1/4. This estimate implies an asymptotic expression for the solution indicating the presence of a track behind the body.
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Translated fromMatematicheskie Zametki, Vol. 65, No. 2, pp. 246–253, February, 1999.
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Sazonov, L.I. Asymptotic behavior of the solution to the two-dimensional stationary problem of flow past a body far from it. Math Notes 65, 202–207 (1999). https://doi.org/10.1007/BF02679817
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DOI: https://doi.org/10.1007/BF02679817