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Finite time singularities in a class of hydrodynamic models

2001
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Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
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Models of inviscid incompressible fluid are considered, with the kinetic energy (i.e., the Lagrangian functional) taking the form L∼∫ k^α| v_k|^2d^3 k in 3D Fourier representation, where α is a constant, 0<α< 1. Unlike the case α=0 (the usual Eulerian hydrodynamics), a finite value of α results in a finite energy for a singular, frozen-in vortex filament. This property allows us to study the dynamics of such filaments without the necessity of a regularization procedure for short length scales.

doi:10.1103/physreve.63.056306
pmid:11415005
fatcat:wjarxefqofavtfkhryojlpt2ra