Front formation in an active scalar equation

Peter Constantin, Qing Nie, and Norbert Schörghofer
Phys. Rev. E 60, 2858 – Published 1 September 1999
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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.

  • Received 21 December 1998


©1999 American Physical Society

Authors & Affiliations

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

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Vol. 60, Iss. 3 — September 1999

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