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6 - Sharp and almost-sharp fronts for the SQG equation

Published online by Cambridge University Press:  05 November 2012

C.L. Fefferman
Affiliation:
Princeton University
James C. Robinson
Affiliation:
University of Warwick
José L. Rodrigo
Affiliation:
University of Warwick
Witold Sadowski
Affiliation:
Uniwersytet Warszawski, Poland
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Publisher: Cambridge University Press
Print publication year: 2012

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References

Bertozzi, A.L. & Constantin, P. (1993) Global regularity for vortex patches. Comm. Math. Phys. 152, no. 1, 19–28.Google Scholar
Caffarelli, L.A. & Vasseur, A. (2010) Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation. Ann. of Math. (2) 171, no. 3, 1903–1930.Google Scholar
Chemin, J.Y. (1993) Persistance de structures géométriques dans les fluides incompressibles bidimensionnels. Ann. Ec. Norm. Supér. 26, no. 4, 1–16.Google Scholar
Constantin, P., Majda, A., & Tabak, E. (1994a) Singular front formation in a model for quasigesotrophic flow. Phys. Fluids 6, no. 1, 9–11.Google Scholar
Constantin, P., Majda, A., & Tabak, E. (1994b) Formation of strong fronts in the 2 – D quasigeostrophic thermal active scalar. Nonlinearity 7, no. 6, 1495–1533.Google Scholar
Córdoba, D., Fefferman, C., & Rodrigo, J.L. (2004) Almost sharp fronts for the surface Quasi-Geostrophic equation. Proc. Natl. Acad. Sci. USA 101, no. 9, 2487–2491.Google Scholar
Córdoba, D., Fontelos, M.A., Mancho, A.M., & Rodrigo, J.L. (2005) Evidence of singularities for a family of contour dynamics equations. Proc. Natl. Acad. Sci. USA 102, no. 17, 5949–5952.Google Scholar
Fefferman, C. & Rodrigo, J.L. (2011) Analytic Sharp Fronts for SQG. Comm. Math. Phys. 303, no. 1, 261–288.Google Scholar
Fefferman, C. & Rodrigo, J.L. (2012) Almost-Sharp Fronts for SQG: the limit equations. Comm. Math. Phys. 313, 131–153.Google Scholar
Fefferman, C., Luli, G., & Rodrigo, J.L. (2012) The spine of an SQG almost sharp front. Nonlinearity 313, 329–342.Google Scholar
Gancedo, F. (2008) Existence for the α-patch model and the QG sharp front in Sobolev spaces. Adv. Math. 217 no. 6, 2569–2598.Google Scholar
Kiselev, A., Nazarov, F., & Volberg, A. (2007) Global well-posedness for the critical 2D dissipative quasi-geostrophic equation. Invent. Math. 167, no. 3, 445–453.Google Scholar
Majda, A.J. & Bertozzi, A.L. (2002) Vorticity and the Mathematical Theory of Incompressible Fluid Flow. Cambridge University Press, Cambridge. England.
Mancho, A.M. (2009) Numerical studies on the self-similar collapse of the alpha-patches problem. arXiv:0902.0706.
Nirenberg, L. (1972) An abstract form of the nonlinear Cauchy–Kowalewski theorem, J. Differential Geom. 6, 561–576.Google Scholar
Rodrigo, J.L. (2004) The vortex patch problem for the Quasi-Geostrophic equation. Proc. Natl. Acad. Sci. USA 101, no. 9, 2484–2486.Google Scholar
Rodrigo, J.L. (2005) On the evolution of sharp fronts for the quasi-geostrophic equation. Comm. Pure Appl. Math. 58, no. 6, 821–866.Google Scholar
Safonov, M.V. (1995) The abstract Cauchy.Kovalevskaya theorem in a weighted Banach space. Comm. Pure and Appl. Math. 48, 629–637.Google Scholar
Sammartino, M. & Caflisch, R.E. (1998a) Zero Viscosity Limit for Analytic Solutions of the Navier–Stokes Equation on a Half-Space I. Existence for Euler and Prandtl equations. Comm. Math. Phys. 192, 433–461.Google Scholar
Sammartino, M. & Caflisch, R.E. (1998b) Zero Viscosity Limit for Analytic Solutions of the Navier–Stokes Equation on a Half-Space II. Construction of Navier–Stokes Solution. Comm. Math. Phys. 192, 463–491.Google Scholar

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