A Blow up Solution of the Navier-Stokes Equations with a Super Critical Forcing Term

Abstract

A forced solution v of the axially symmetric Navier-Stokes equation in a finite cylinder D with suitable boundary condition is constructed. The forcing term, whose order of scaling is slightly worse than the critical order −2, is in the mildly super critical space L^q_t L¹_x for all q>1. The velocity, which is smooth until its final blow up moment, is in the energy space throughout.

Keywords

Navier-Stokes equations / blow up example with supercritical forcing term