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

TY - JOUR

T1 - Construction of Almost-Sharp Fronts for the Surface Quasi-Geostrophic Equation

AU - Fefferman, Charles L.

AU - Rodrigo, José L.

N1 - Publisher Copyright: © 2015, Springer-Verlag Berlin Heidelberg.

PY - 2015/10/27

Y1 - 2015/10/27

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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U2 - 10.1007/s00205-015-0857-y

DO - 10.1007/s00205-015-0857-y

M3 - Article

SN - 0003-9527

VL - 218

SP - 123

EP - 162

JO - Archive For Rational Mechanics And Analysis

JF - Archive For Rational Mechanics And Analysis

IS - 1

ER -