∂ ρ ∂ t + ∇ ⋅ ( ρ u ) = 0 , {\displaystyle {\frac {\partial \rho }{\partial t}}+\nabla \cdot \left(\rho \mathbf {u} \right)=0\,,} ∂ ( ρ u ) ∂ t + ∂ ∂ x ( ρ u 2 + p ) + ∂ ∂ y ( ρ u v ) = 0 , {\displaystyle {\frac {\partial (\rho u)}{\partial t}}+{\frac {\partial }{\partial x}}\left(\rho u^{2}+p\right)+{\frac {\partial }{\partial y}}\left(\rho uv\right)=0\,,}
