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The Navier-Stokes equations on a bounded domain

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Abstract

SupposeU is an open bounded subset of 3-space such that the boundary ofU has Lebesgue measure zero. Then for any initial condition with finite kinetic energy we can find a global (i.e. for all time) weak solutionu to the time dependent Navier-Stokes equations of incompressible fluid flow inU such that the curl ofu is continuous outside a locally closed set whose 5/3 dimensional Hausdorff measure is finite.

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Communicated by J. Glimm

This research was supported in part by the National Science Foundation Grant MCS-7903361

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Scheffer, V. The Navier-Stokes equations on a bounded domain. Commun.Math. Phys. 73, 1–42 (1980). https://doi.org/10.1007/BF01942692

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  • DOI: https://doi.org/10.1007/BF01942692

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