We present some ways to modify the incompressible Navier-Stokes and Euler equations in three dimensions in order to permit solutions that blow up in finite time. For Navier-Stokes, we replace the transport term by an averaged version of that term of equal or lesser "strength" from the point of view of function space estimates, while still retaining the energy identity. For Euler, we modify the vorticity-stream relation to a pseudodifferential operator of the same order, while still retaining the conservation of circulation, energy, helicity, and vortex stream lines.
Copyright. All Rights Reserved.