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Solutions to 3-dimensional Navier-Stokes equations for incompressible fluid

By Jorma Jormakka

Abstract

Abstract. This paper gives an example of a periodic, smooth, divergencefree initial vector field and a periodic and bounded external force such that there exist a smooth solution to the 3-dimensional Navier-Stokes equations for incompressible fluid with those initial conditions but the solution cannot be continued to the whole space. The example also shows that the solutions to the Navier-Stokes equations are not unique

Topics: Key words, Partial differential equations, Navier-Stokes equation, fluid dynamics. Subject Classifications, 35Q30
OAI identifier: oai:CiteSeerX.psu:10.1.1.311.8680
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