NONEXISTENCEOFSMOOTH SOLUTIONS FOR SHEARINGFLOWS IN A NONLINEARVISCOELASTIC FLUID

f Abstract. This paper studies the development of singularities in smooth solutions of an equation arising from a perturbation problem for steady sheafing flows in a nonlinear viscoelastic fluid. It is proved that under certain assumptions (that make the equation studied nonlinear), singularities will develop in the derivatives of the velocity of the flow, provided that some derivatives of the initial data are sufficiently large.