On the Role of the Convection Term in the Equations of Motion of Incompressible Fluid

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Abstract

We consider the equations of motion of incompressible fluid. Several examples of blow-up for model equations are studied in order to suggest that the existence of the convection term plays a crucial role in the global existence of smooth solutions of some equations including the two-dimensional Euler equations. If we may say so, the convection term suppresses the blow-up of solutions.

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