Blow ups of complex solutions of the 3D Navier-Stokes system and renormalization group method

Dong Li; Ya G. Sinai

doi:10.4171/JEMS/111

Blow ups of complex solutions of the 3D Navier-Stokes system and renormalization group method

Dong Li, Ya G. Sinai

Research output: Contribution to journal › Article › peer-review

50 Scopus citations

Abstract

We consider complex-valued solutions of the three-dimensional Navier-Stokes system without external forcing on ℝ³. We show that there exists an open set in the space of 10-parameter families of initial conditions such that for each family from this set there are values of parameters for which the solution develops blow up in finite time.

Original language	English (US)
Pages (from-to)	267-313
Number of pages	47
Journal	Journal of the European Mathematical Society
Volume	10
Issue number	2
DOIs	https://doi.org/10.4171/JEMS/111
State	Published - 2008

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

Keywords

Fixed point
Hermite polynomials
Linearization near a fixed point
Navier-Stokes system
Renormalization group theory
Spectrum of the linearized group

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10.4171/JEMS/111

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abstract = "We consider complex-valued solutions of the three-dimensional Navier-Stokes system without external forcing on ℝ3. We show that there exists an open set in the space of 10-parameter families of initial conditions such that for each family from this set there are values of parameters for which the solution develops blow up in finite time.",

keywords = "Fixed point, Hermite polynomials, Linearization near a fixed point, Navier-Stokes system, Renormalization group theory, Spectrum of the linearized group",

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AU - Sinai, Ya G.

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AB - We consider complex-valued solutions of the three-dimensional Navier-Stokes system without external forcing on ℝ3. We show that there exists an open set in the space of 10-parameter families of initial conditions such that for each family from this set there are values of parameters for which the solution develops blow up in finite time.

KW - Fixed point

KW - Hermite polynomials

KW - Linearization near a fixed point

KW - Navier-Stokes system

KW - Renormalization group theory

KW - Spectrum of the linearized group

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Blow ups of complex solutions of the 3D Navier-Stokes system and renormalization group method

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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