Front formation in an active scalar equation.
We study the formation of thermal fronts in an active scalar equation that is similar to the Euler equation. For a particular initial condition, an earlier candidate for finite-time blowup, the front forms in a generalized self-similar way with constant hyperbolicity at the center. The behavior belongs to a class of scenarios for which finite-time blowup is impossible. A systematic exploration of many different initial conditions reveals no evidence of singular solutions.
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