What restrictions or conditions are imposed on stream function ? so that it exactly satisfies the two-dimensional incompressible continuity equation by definition? Why are these restrictions necessary?

Engineering Fundamentals: An Introduction to Engineering (MindTap Course List)
5th Edition
ISBN:9781305084766
Author:Saeed Moaveni
Publisher:Saeed Moaveni
Chapter18: Mathematics In Engineering
Section: Chapter Questions
Problem 9P
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What restrictions or conditions are imposed on stream function ? so that it exactly satisfies the two-dimensional incompressible continuity equation by definition? Why are these restrictions necessary?

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