title: Front formation in an active scalar equation.
abstract: 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.
authors.affiliation: Department of Mathematics, The University of Chicago, 5734 South University Avenue, Chicago, Illinois 60637, USA.
authors.forename: P
authors.initials: P
authors.lastname: Constantin
authors.forename: Q
authors.initials: Q
authors.lastname: Nie
authors.forename: N
authors.initials: N
authors.lastname: Schörghofer