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Structural stability for the splash singularities of the water waves problem
December 2014, 34(12): 5045-5059. doi: 10.3934/dcds.2014.34.5045
Remarks on geometric properties of SQG sharp fronts and $\alpha$-patches
Angel Castro 1, , Diego Córdoba 2, , Javier Gómez-Serrano 3, and Alberto Martín Zamora 2,
Departamento de Matemáticas de la UAM, Instituto de Ciencias Matemáticas del CSIC, Campus de Cantoblanco, 28049 Madrid, Spain
Instituto de Ciencias Matemáticas, Consejo Superior de Investigaciones Científicas, C/ Nicolas Cabrera, 13-15, 28049 Madrid, Spain, Spain
Department of Mathematics, Princeton University, 1102 Fine Hall, Washington Rd, Princeton, NJ 08544, United States
Received January 2014 Revised May 2014 Published June 2014
Guided by numerical simulations, we present the proof of two results concerning the behaviour of SQG sharp fronts and $\alpha$-patches. We establish that ellipses are not rotational solutions and we prove that initially convex interfaces may lose this property in finite time.
Keywords: computer-assisted, patches., contour dynamics, Surface quasigeostrophic, incompressible flow.
Mathematics Subject Classification: Primary: 76B47, 35Q31; Secondary: 65G3.
Citation: Angel Castro, Diego Córdoba, Javier Gómez-Serrano, Alberto Martín Zamora. Remarks on geometric properties of SQG sharp fronts and $\alpha$-patches. Discrete & Continuous Dynamical Systems - A, 2014, 34 (12) : 5045-5059. doi: 10.3934/dcds.2014.34.5045
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Angel Castro Diego Córdoba Javier Gómez-Serrano Alberto Martín Zamora