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.

arXiv comment111 pages, 3 figures

References in corpus (16)

• Invariant manifolds and the long-time asymptotics of the Navier-Stokes and vorticity equations on R^2
• Dynamic Depletion of Vortex Stretching and Non-Blowup of the 3-D Incompressible Euler Equations
• Long-time asymptotics of the Navier-Stokes and vorticity equations on R^3
• The defocusing energy-critical nonlinear Schrödinger equation in higher dimensions
• On the global wellposedness of the 3-D Navier-Stokes equations with large initial data
• Fine properties of self-similar solutions of the Navier-Stokes equations
• Probability & incompressible Navier-Stokes equations: An overview of some recent developments
• Five types of blow-up in a semilinear fourth-order reaction-diffusion equation: an analytic-numerical approach
• Computational Euler History
• Ortho-normal quaternion frames, Lagrangian evolution equations and the three-dimensional Euler equations
• Nonexistence of Local Self-Similar Blow-up for the 3D Incompressible Navier-Stokes Equations
• On Landau's Solutions of the Navier-Stokes Equations
• Implementation for blow up of tornado-type solutions for complex version of 3D Navier-Stokes system
• On the Analyticity of Solutions to the Navier-Stokes Equations with Fractional Dissipation
• Liouville theorems for the Navier-Stokes equations and applications
• On the behaviors of solution near possible blow-up time in the incompressible Euler and related equations

Cited by in corpus (9)

• Five types of blow-up in a semilinear fourth-order reaction-diffusion equation: an analytic-numerical approach
• $L^2$-asymptotic stability of mild solutions to Navier-Stokes system in $R^3$
• Boundary Characteristic Point Regularity for Navier-Stokes Equations: Blow-up Scaling and Petrovskii-type Criterion (a Formal Approach)
• Time-dependent singularities in the Navier-Stokes system
• 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
• Stability of singular solutions to the Navier-Stokes system
• Exact Solutions on Twisted Rings for the 3D Navier-Stokes Equations
• Sturmian Multiple Zeros for Stokes and Navier--Stokes Equations in $\re^3$ via Solenoidal Hermite Polynomials