, Volume 101, Issue 1, pp 47-85

A solution to the Navier-Stokes inequality with an internal singularity

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Abstract

We consider weak solutions to the time dependent Navier-Stokes equations of incompressible fluid flow in three dimensional space with an external force that always acts against the direction of the flow. We show that there exists a solution with an internal singularity. The speed of the flow reaches infinity at this singular point. In addition, the solution has finite kinetic energy.

The author was supported in part by a Sloan Foundation Fellowship
Communicated by L. Nirenberg