The new exact solution of the compressible 3D Navier–Stokes equations

Abstract

The new exact solution of the compressible 3D Navier-Stokes (NS) equations in the case of zero shear viscosity η=0and finite volume viscosityςis obtained. It gives the possibility to avoid the closure problem and has finite time singularity att=t0 which is depended on initial velocity. The regularization of this singularity is possible due to the introduction of a super threshold homogeneous friction (unavoidable arising in all numerical simulations with NS equations) μ=νlmin2>μth=1/t0or by taking into account of any small shear viscosityν=η/ρ0>0;ν=const. This also gives the unexpectedly positive answer on the generalization of the Millennium Prize Problem for the case of compressible Navier-Stokes equations www.claymath.org.