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Openai/6935580c-34e4-8001-9136-7bbdf1499790
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==== The mild formulation is extremely useful because it converts the PDE into an integral fixed-point equation (Picard iteration / contraction mapping), and because the heat semigroup eνtΔe^{\nu t\Delta}eνtΔ provides explicit smoothing estimates used to control the nonlinear term. The steps above show precisely how the pressure is eliminated (via projection), how Duhamel’s formula is derived, and how to reconstruct the pressure from a mild solution. ====
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