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The concentration phenomenon of the kinetic energy, (rho |mathbf{u}|^2), associated to isentropic compressible Navier–Stokes equations, is addressed  ({mathbb {R}}^n) with (n=2,3) and the adiabatic constant (gamma in [1,frac{n}{2}]). Except for a space-time set with a Hausdorff dimension of less than or equal to (Gamma (n)+1) with $$begin{aligned} Gamma (n)=max left{ gamma (n), n-frac{ngamma }{gamma (n)+1}right} quad {text {and}}quad gamma (n)=frac{n(n-1)-ngamma }{n-gamma }, end{aligned}$$no concentration phenomenon occurs.

Hausdorff Dimension of Concentration for Isentropic Compressible Navier–Stokes Equations