On blow-up "twistors" for the Navier--Stokes equations in $R^3$: a view from reaction-diffusion theory

Details On blow-up "twistors" for the Navier--Stokes equations in $R^3$: a view from reaction-diffusion theory On blow-up "twistors" for the Navier--Stokes equations in $R^3$: a view from reaction-diffusion theory

2009-01-27

arxiv.org/abs/0901.4286v1

Mathematics

Analysis of PDEs

111 pages, 3 figures

Scientific paper

Various formal blow-up scenarious for the Navier--Stokes equaitons in 3D are discussed. A particular interest is payed to "twistor mechanisms" based on angular logarithmic blow-up travelling waves, and to a formation of "blow-up tornado" about the singular stationary Slezkin--Landau solutions (1934--44) of a submerged jet. A survey on various related aspects of singularity analysis for nonlinear parabolic PDEs is enclosed.

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