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.
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Communicated by L. Nirenberg
The author was supported in part by a Sloan Foundation Fellowship
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Scheffer, V. A solution to the Navier-Stokes inequality with an internal singularity. Commun.Math. Phys. 101, 47–85 (1985). https://doi.org/10.1007/BF01212356
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DOI: https://doi.org/10.1007/BF01212356