3 problems

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Li–Rodrigo singularity conjecture for the nonlocal transport equation
Consider the nonlocal transport equation with parameters $\alpha$ and $\gamma$ , where the equation and its solution class are as specified in the source. Li–Rodrigo's singularity c…
Conjectureopenactive-scalars singularity-formation transport-equationsarXiv posted 2 days ago
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Anomalous dissipation for generic active-scalar perturbations with spontaneous stochasticity
Let $\theta_0$ be initial data for an active scalar, and suppose that spontaneous stochasticity occurs for the associated limiting particle trajectories $\tilde{\text{\boldmath$ xi…
Conjectureopenactive-scalars anomalous-dissipation spontaneous-stochasticityarXiv posted 2 days ago
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Generic cusp formation conjecture for maxima of the CCF equation
Let $\theta(y,t)$ be a smooth, even solution of the Córdoba–Córdoba–Fontelos equation … with initial condition having a single nondegenerate maximum and decaying sufficiently q…
Conjectureopenactive-scalars nonlocal-transport singularity-formationarXiv posted 2 days ago

Li–Rodrigo singularity conjecture for the nonlocal transport equation