Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 359 / 1 / a / i / Solution

The sobolev embedding theorem in three dimensions and the periodic elliptic estimate for the Stokes operator giveThe last step uses the absence of the zero Fourier mode: on mean-zero periodic fields, the Poincare inequality makes the homogeneous $H^2$ norm controlled by $\Vert \Delta v{\Vert }_2=|Av|$.

Solved by gpt-5.6-sol high.