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Partial regularity of a generalized solution to the Navier-Stokes equations in exterior domain

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In this note, we prove two regularity theorems for solutions to the Navier-Stokes equations of an I.B.V.P. in exterior domains. Namely, we prove that the setS of the singular points of a solution, if not empty, has at most 1-Hausdorff measureH 1(S)=0. Moreover, the setS is enclosed in a sphere of rayR for anyt>0. These results are obtained as corollaries to the partial regularity results furnished in [2].

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Communicated by C. H. Taubes

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Maremonti, P. Partial regularity of a generalized solution to the Navier-Stokes equations in exterior domain. Commun.Math. Phys. 110, 75–87 (1987). https://doi.org/10.1007/BF01209017

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