Concentrations problem for solutions to compressible Navier–Stokes equations

A three-dimensional initial-boundary value problem for the isentropic equations of the dynamics of a viscous gas is considered. The concentration phenomenon is that, for adiabatic exponent values $\gamma\le3/2$, the finite energy can be concentrated on arbitrarily small sets. It is proved that, in the critical case $\gamma=3/2$, the norm of the density of kinetic energy in the logarithmic Orlicz space is bounded by a constant that depends only on the initial and boundary data. This eliminates the possibility of the concentration phenomenon.