Time-dependent singularities in the Navier-Stokes system

Abstract

We show that, for a given Hölder continuous curve in $\{(\gamma (t),t):t>0\}\subset R^3\times R^{+}$, there exists a solution to the Navier-Stokes system for an incompressible fluid in $R^3$ 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 $R^3\times R^{+}$, it solves an analogous Navier-Stokes system with a singular force concentrated on the curve.

20 pages

References in corpus (3)

• On blow-up "twistors" for the Navier--Stokes equations in $R^3$: a view from reaction-diffusion theory
• $L^2$-asymptotic stability of mild solutions to Navier-Stokes system in $R^3$
• Regularity criteria in weak $L^3$ for 3D incompressible Navier-Stokes equations