We show that by ‘accelerating’ relaxation enhancing flows, one can construct a flow that is smooth on [ 0 , 1 ) × T d but highly singular at t = 1 so that for any positive diffusivity, the advection–diffusion equation associated to the accelerated flow totally dissipates solutions, taking arbitrary initial data to the constant function at t = 1.
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Keefer Rowan (2024) studied this question.
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