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

Vladimir Scheffer

doi:10.1007/BF01212356

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

Vladimir Scheffer

School of Arts and Sciences, Mathematics

Research output: Contribution to journal › Article › peer-review

18 Scopus citations

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.

Original language	English (US)
Pages (from-to)	47-85
Number of pages	39
Journal	Communications In Mathematical Physics
Volume	101
Issue number	1
DOIs	https://doi.org/10.1007/BF01212356
State	Published - Mar 1985

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/BF01212356

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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.",

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

Abstract

All Science Journal Classification (ASJC) codes

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