Formation of blow-up singularities for the Navier–Stokes equations and in is studied. In cylindrical polar coordinates in , their restriction to the linear subspace is shown to be consistent. Using links with blow-up theory for nonlinear reaction-diffusion partial differential equations, the following questions are under scrutiny: (ii) introducing a self-similar blow-up “swirl mechanism” with the angular swirl divergences and as , where is a parameter; (ii) existence of a countable family of space jets via a nonlocal semilinear parabolic equation with effective regional/global blow-up of the component of the velocity; (iii) as an intrinsic part of the construction, convergence of the above rescaled patterns as to smooth blow-up self-similar solutions of the corresponding three-dimensional Euler equations and in , which (iv) are also shown to admit single point blow-up in the similarity variables.
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November 2008
Research Article|
November 06 2008
On blow-up space jets for the Navier–Stokes equations in with convergence to Euler equations
V. A. Galaktionov
V. A. Galaktionov
a)
Department of Mathematical Sciences,
University of Bath
, Bath BA2 7AY, United Kingdom
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a)
Electronic mail: [email protected].
J. Math. Phys. 49, 113101 (2008)
Article history
Received:
January 18 2008
Accepted:
October 08 2008
Citation
V. A. Galaktionov; On blow-up space jets for the Navier–Stokes equations in with convergence to Euler equations. J. Math. Phys. 1 November 2008; 49 (11): 113101. https://doi.org/10.1063/1.3012382
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