Three-dimensional forced Burgers turbulence supplemented with a continuity equation

We investigate turbulent limit of the forced Burgers equation supplemented with a continuity equation in three dimensions. The scaling exponent of the conditional two-point correlation function of density, i.e., [rho (x(1))rho (x(2))\ Deltau] similar to \x(1) - x(2)\(-alpha3), is calculated self-consistently in the nonuniversal region from which we obtain alpha (3)=3 Also we derive an equation governing the evolution of the probability density function (PDF) of longitudinal velocity increments in length scale, from which a possible mechanism for the dependence of the inertial PDF to one-point u(rms) is developed.