We study a coarse-grained asymptotic equation which describes deformation of vortex lattices [Smirnov & Chukbar 2001]. It reads Φ_t = Φ_(xx)Φ_(yy) - Φ_(xy)~2, where Φ denotes displacement of vortex locations. This equation is valid for a lattice with short-ranged interaction, e.g. geostrophic vortices with a screened potential. New self-similar blow-up solutions with infinite total energy are found. We ask whether or not finite-time blow-up can take place developing from smooth initial data with finite energy. The numerical simulations show finite-time blow-up in such a way that Φ ∈ H~3 but Φ /∈ H~4.
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