The spine of an SQG almost-sharp front

Charles Fefferman; Garving Luli; Jose Rodrigo

doi:10.1088/0951-7715/25/2/329

The spine of an SQG almost-sharp front

Charles Fefferman, Garving Luli, Jose Rodrigo

Mathematics

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

13 Scopus citations

Abstract

We study solutions of the surface quasi-geostrophic (SQG) equation which are locally constant outside a thin neighbourhood of a curve that evolves with time. To such an SQG solution we associate a distinguished curve (the 'spine'). If the above thin neighbourhood has thickness δ, then we prove that the spine satisfies its own evolution equation (equal to the sharp-front equation) modulo errors O(δ ²|logδ|).

Original language	English (US)
Pages (from-to)	329-342
Number of pages	14
Journal	Nonlinearity
Volume	25
Issue number	2
DOIs	https://doi.org/10.1088/0951-7715/25/2/329
State	Published - Feb 2012

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics
General Physics and Astronomy
Applied Mathematics

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10.1088/0951-7715/25/2/329

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title = "The spine of an SQG almost-sharp front",

abstract = "We study solutions of the surface quasi-geostrophic (SQG) equation which are locally constant outside a thin neighbourhood of a curve that evolves with time. To such an SQG solution we associate a distinguished curve (the 'spine'). If the above thin neighbourhood has thickness δ, then we prove that the spine satisfies its own evolution equation (equal to the sharp-front equation) modulo errors O(δ 2|logδ|).",

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AB - We study solutions of the surface quasi-geostrophic (SQG) equation which are locally constant outside a thin neighbourhood of a curve that evolves with time. To such an SQG solution we associate a distinguished curve (the 'spine'). If the above thin neighbourhood has thickness δ, then we prove that the spine satisfies its own evolution equation (equal to the sharp-front equation) modulo errors O(δ 2|logδ|).

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The spine of an SQG almost-sharp front

Abstract

All Science Journal Classification (ASJC) codes

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