Consider inviscid incompressible flow with constant density $0=1.$ Show that the pressure satisfies the Poisson equation $$p $=|$S$|2|$D$|2,$ where $$u $=$ D $+$ S$,$ D is the deformation matrix, S is the rotation matrix, and $|$S$|2,|$D$|2$ denote the sum of squares of the matrix elements. $($This is consistent with the results of problem $1$ on hw$2$ showing that strain is a source of high pressure and vorticity is a source of low pressure.$)$