Past exam of the mathematics course of the University of Cambridge / 2021 / ii / Paper 1 / 39A / a

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- Solution a

Solution

For an incompressible Newtonian fluid with negligible inertia and no body force, the Stokes equations are

- \nabla p + μ \nabla^{2} u = 0, \nabla \cdot u = 0 .

They are linear because any linear combination of solutions corresponds to the same linear combination of boundary data and applied forces. They are reversible because replacing all imposed velocities and forces by their negatives sends

(u, p) ⟼ (- u, - p) .

Fluid particles therefore retrace their paths under reversal. This is kinematic reversibility of Stokes flow.

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