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Infinite energy solutions of the surface quasi-geostrophic equation. (English) Zbl 1205.35219
The authors study the formation of singularities of a 1D nonlinear and non-local (surface quasi-geostrophic, SQG) equation, which is also a model for 3D vorticity Euler equations. One shows that this equation provides solutions of the surface quasi-geostrophic equation with infinite energy. The existence of self-similar solutions and the blow-up for classical solutions are also shown.

35Q35 PDEs in connection with fluid mechanics
35Q31 Euler equations
76B47 Vortex flows for incompressible inviscid fluids
76E30 Nonlinear effects in hydrodynamic stability
35B40 Asymptotic behavior of solutions to PDEs
35B65 Smoothness and regularity of solutions to PDEs
Full Text: DOI
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