Construction of Almost-Sharp Fronts for the Surface Quasi-Geostrophic Equation

Charles L. Fefferman; José L. Rodrigo

doi:10.1007/s00205-015-0857-y

Construction of Almost-Sharp Fronts for the Surface Quasi-Geostrophic Equation

Charles L. Fefferman, José L. Rodrigo

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

In this paper we construct families of real analytic solutions of the Surface Quasi-Geostrophic equation (SQG) that are locally constant outside a thin neighborhood of a curve of arbitrarily small thickness. Despite the fact that only local existence results are known for SQG, and that our initial conditions have a arbitrarily large gradient we show that solutions exist for a time independent of the thickness of the neighborhood.

Original language	English (US)
Pages (from-to)	123-162
Number of pages	40
Journal	Archive for Rational Mechanics and Analysis
Volume	218
Issue number	1
DOIs	https://doi.org/10.1007/s00205-015-0857-y
State	Published - Oct 27 2015
Externally published	Yes

All Science Journal Classification (ASJC) codes

Analysis
Mathematics (miscellaneous)
Mechanical Engineering

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10.1007/s00205-015-0857-y

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abstract = "In this paper we construct families of real analytic solutions of the Surface Quasi-Geostrophic equation (SQG) that are locally constant outside a thin neighborhood of a curve of arbitrarily small thickness. Despite the fact that only local existence results are known for SQG, and that our initial conditions have a arbitrarily large gradient we show that solutions exist for a time independent of the thickness of the neighborhood.",

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AU - Rodrigo, José L.

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N2 - In this paper we construct families of real analytic solutions of the Surface Quasi-Geostrophic equation (SQG) that are locally constant outside a thin neighborhood of a curve of arbitrarily small thickness. Despite the fact that only local existence results are known for SQG, and that our initial conditions have a arbitrarily large gradient we show that solutions exist for a time independent of the thickness of the neighborhood.

AB - In this paper we construct families of real analytic solutions of the Surface Quasi-Geostrophic equation (SQG) that are locally constant outside a thin neighborhood of a curve of arbitrarily small thickness. Despite the fact that only local existence results are known for SQG, and that our initial conditions have a arbitrarily large gradient we show that solutions exist for a time independent of the thickness of the neighborhood.

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Construction of Almost-Sharp Fronts for the Surface Quasi-Geostrophic Equation

Abstract

All Science Journal Classification (ASJC) codes

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