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Up to now, it is unknown an existence of blow up solutions in the Cauchy problem for Navier–Stokes equations in space. The first important property of hypothetical blow up solutions was found by J. Leray in 1934. It is connected with norms in Lp(R3),p>3. However, there are important solutions in L2(R3) because the second power of this norm can be interpreted as a kinetic energy of the fluid flow. It gives a new possibility to study an influence of kinetic energy changing on solution properties. There are offered new tools in this way. In particular, inequalities with an invariant form are considered as elements of latent symmetry.

Some Properties of Blow up Solutions in the Cauchy Problem for 3D Navier–Stokes Equations