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

Abstract

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.

111 pages, 3 figures

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• On the Analyticity of Solutions to the Navier-Stokes Equations with Fractional Dissipation
• Liouville theorems for the Navier-Stokes equations and applications
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Cited by in corpus (2)

• On global solutions and blow-up for Kuramoto-Sivashinsky-type models, and well-posed Burnett equations
• Three tupes of self-similar blow-up for the fourth-order p-Laplacian equaiton with source: variational and branching approaches