 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2026/iii/paper-359/1/b/i/solution

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

Both

P_{m}

L^{2}

. Taking the

H

norm of the first Galerkin equation gives

ν ∣ A u_{m} ∣ = α ∣ P_{m} P_{σ} (θ_{m} e_{3}) ∣ \leq α ∥ θ_{m} e_{3} ∥_{2} = α ∥ θ_{m} ∥_{2} .

Therefore

∣ A u_{m} ∣ \leq \frac{α}{ν} ∥ θ_{m} ∥_{2} .

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