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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.
MSC:
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
Software:
SQG
References:
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