Pressureless gas equations with viscosity and nonlinear diffusion

Under some regularity conditions on P-0 and u(0), we derive a unique local strong solution of the following system of pressureless gas equations with viscosity: [GRAPHICS] P-t-->P-0, uP(t) --> u(0)P(0), weakly, as t --> 0(+), by constructing a nonlinear diffusion process as solution to the following SDE: [GRAPHICS] We show then that Pt is the probability density of X-t while the velocity field admits the Following stochastic representation: u(t,X) = E [u(0)(X-0) \ X-t = x]. (C) 2001 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.