Let us consider the Cauchy problem
in QT= ℝ3 × [0, T], where f(x, t), ρ0(x) and v0(x) are given, while the density ρ(x, t), the velocity vector v(x, t)= (υ1(x, t), υ2(x, t), υ3(x, t)) and the pressure p(x, t) are unknowns. The viscosity coefficient μ is assumed to be nonnegative. In these equations, the pressure p is automatically determined (up to a function of t) by ρ and v, namely, by solving the equation
Thus we mention (ρ, v) when we talk about the solution of (1.1:μ).