Self-Similar Solutions of Leray’s Type for Compressible Navier-Stokes Equations in Two Dimension

We study the backward self-similar solution of Leray's type for compressible Navier-Stokes equations in dimension two.The existence of weak solutions is established via a compactness argument with the help of an higher integrability of density.Moreover, if the density belongs to L ∞ (R 2 ) and the velocity belongs to L 2 (R 2 ), the solution is trivial; that is (ρ,u) = 0.