# 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. [copyright] [ital 1999] [ital The American Physical Society]

- Authors:

- (Department of Mathematics, The University of Chicago, 5734 South University Avenue, Chicago, Illinois 60637 (United States))
- (James Franck Institute, The University of Chicago, 5640 South Ellis Avenue, Chicago, Illinois 60637 (United States))

- Publication Date:

- OSTI Identifier:
- 6466347

- Alternate Identifier(s):
- OSTI ID: 6466347

- Resource Type:
- Journal Article

- Journal Name:
- Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

- Additional Journal Information:
- Journal Volume: 60:3; Journal ID: ISSN 1063-651X

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; FLUID FLOW; PARTIAL DIFFERENTIAL EQUATIONS; SCALAR FIELDS; TEMPERATURE DISTRIBUTION; DIFFERENTIAL EQUATIONS; EQUATIONS 661300* -- Other Aspects of Physical Science-- (1992-)

### Citation Formats

```
Constantin, P., Nie, Q., and Schoerghofer, N.
```*Front formation in an active scalar equation*. United States: N. p., 1999.
Web. doi:10.1103/PhysRevE.60.2858.

```
Constantin, P., Nie, Q., & Schoerghofer, N.
```*Front formation in an active scalar equation*. United States. doi:10.1103/PhysRevE.60.2858.

```
Constantin, P., Nie, Q., and Schoerghofer, N. Wed .
"Front formation in an active scalar equation". United States. doi:10.1103/PhysRevE.60.2858.
```

```
@article{osti_6466347,
```

title = {Front formation in an active scalar equation},

author = {Constantin, P. and Nie, Q. and Schoerghofer, N.},

abstractNote = {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. [copyright] [ital 1999] [ital The American Physical Society]},

doi = {10.1103/PhysRevE.60.2858},

journal = {Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics},

issn = {1063-651X},

number = ,

volume = 60:3,

place = {United States},

year = {1999},

month = {9}

}

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