Explicit solutions of the viscous model vorticity equation

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<jats:title>Abstract</jats:title><jats:p>Explicit solutions are found for the viscous version of the model vorticity equation recently proposed by P. Constantin, P. D. Lax, and A. Majda: <jats:disp-formula> </jats:disp-formula> where <jats:italic>H</jats:italic>(<jats:italic>w</jats:italic>) is the Hilbert transform of <jats:italic>w</jats:italic>, and <jats:italic>v</jats:italic> is a positive constant. Various properties of these solutions, including the fact that they blow up after a finite time, are discussed.</jats:p>

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