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Some thoughts on the role of the convection terms in the fluid mechanical PDEs.

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NWWW01 - Nonlinear water waves

Nonlinear PDEs appearing in fluid mechanics often have a convection term, whose role is not well-understood in my viewpoint. I want to state some problems which I cannot answer and wish to usher in young people who may solve them. A key theme is that the convection term prevents the solution from blowing-up. I want to demonstrate this `proposition' by examples.  

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