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Phys. Rev. E 60, 2858 - 2863 (1999)

Front formation in an active scalar equation

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Peter Constantin and Qing Nie
Department of Mathematics, The University of Chicago, 5734 South University Avenue, Chicago, Illinois 60637

Norbert Schörghofer
James Franck Institute, The University of Chicago, 5640 South Ellis Avenue, Chicago, Illinois 60637

Received 21 December 1998

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.


©1999 The American Physical Society

URL: http://link.aps.org/doi/10.1103/PhysRevE.60.2858
DOI: 10.1103/PhysRevE.60.2858
PACS: 47.10.+g, 02.60.-x

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