  We investigate the non-perturbative results of multi-dimensional forced
Burgers equation coupled to the continuity equation. In the inviscid limit, we
derive the exact exponents of two-point density correlation functions in the
universal region in arbitrary dimensions. We then find the universal generating
function and the tails of the probability density function (PDF) for the
longitudinal velocity difference. Our results exhibit that in the inviscid
limit, density fluctuations affect the master equation of the generating
function in such a way that we can get a positive PDF with the well-known
exponential tail. The exponent of the algebraic tail is derived to be -5/2 in
any dimension. Finally we observe that various forcing spectrums do not alter
the power law behaviour of the algebraic tail in these dimensions, due to a
relation between forcing correlator exponent and the exponent of the two-point
density correlation function.
