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)}.
Schauder estimates for parabolic equations with degenerate or singular weights
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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)}.