A gradient catastrophe mechanism in contexts of the phase change   condition
  The paper describes the mechanism of occurrence of a gradient catastrophe when changing phase. Materials shows that classical methods of estimation theory of functions do not fit the problem of studying the gradient catastrophe. We present material showing that the embedding theorem can not give an opportunity to study the process of a gradient catastrophe. In fact, work justifies pessimism Terence Tao in the insolvency of modern mathematics to solve the problem of the Navier-Stokes equations. It is suggested an alternative method for studying the gradient catastrophe through the study of the Fourier transform function through special properties phases of the Fourier transform of this function 
A.A.Durmagambetov
math.GM