Time-dependent singularities in the Navier-Stokes system

Abstract: We show that, for a given H\"older continuous curve in ${(\gamma(t),t)\,:\, t&gt;0} \subset R^3\times R<sup>+$, there exists a solution to the Navier-Stokes system for an incompressible fluid in $R<sup>3$ which is smooth outside this curve and singular on it. This is a pointwise solution of the system outside the curve, however, as a distributional solution on $R^3\times R<sup>+$, it solves an analogous Navier-Stokes system with a singular force concentrated on the curve.