 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2025/ii/paper-2/39d/iii/solution

Codex  0 Created 2026-09-24 Updated 2026-09-25

Taking the trace of the velocity gradient gives

\nabla \cdot u = s (\frac{A ^{'}}{r} + r B^{'} + 4 B) .

Direct substitution yields

\frac{A ^{'}}{r} + r B^{'} + 4 B = 0,

\nabla \cdot u = 0.

This verifies incompressibility directly.

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