The $\alpha$-patch model is used to study aspects of fluid equations. We show that solutions of this model form singularities in finite time and give a characterization of the solution profile at the singular time.
A Nonlocal Transport Equation Describing Roots of Polynomials Under Differentiation
A Wasserstein norm for signed measures, with application to nonlocal transport equation with source term
Global-in-space stability of singularity formation for Yang-Mills fields in higher dimensions
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