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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.
35Q35PDEs in connection with fluid mechanics
35Q31Euler equations
76B47Vortex flows
76E30Nonlinear effects (fluid mechanics)
35B40Asymptotic behavior of solutions of PDE
35B65Smoothness and regularity of solutions of PDE
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