Random turbulent velocity fields cause generic scalar fields to dissipate energy and instantly regularize to sharp fractional regularity, with particle dispersion obeying t^{1/(1-alpha)}.
Fourier analysis and nonlinear partial differential equations , volume 343 of Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]
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Anomalous dissipation and regularization in isotropic Gaussian turbulence
Random turbulent velocity fields cause generic scalar fields to dissipate energy and instantly regularize to sharp fractional regularity, with particle dispersion obeying t^{1/(1-alpha)}.