We propose a one-dimensional model for the vorticity equation involving viscos-ity. Complex methods are utilzed in order to study finite time blow-up of the solutions. In particular, it is shown that the blow-up time depends monotoneously on the viscosity.
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Elias Wegert, A.S. Vasudeva Murthy, Blow-Up in a Modified Constantin-Lax-Majda Model for the Vorticity Equation. Z. Anal. Anwend. 18 (1999), no. 2, pp. 183–191