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., approximately /x1-x2/(-alpha3), is calculated self-consistently in the nonuniversal region from which we obtain alpha3=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.