Complex Singular Solutions of the 3-d Navier–Stokes Equations and Related Real Solutions

Carlo Boldrighini; Dong Li; Yakov G. Sinai

doi:10.1007/s10955-017-1730-1

Complex Singular Solutions of the 3-d Navier–Stokes Equations and Related Real Solutions

Carlo Boldrighini, Dong Li, Yakov G. Sinai

Research output: Contribution to journal › Review article › peer-review

2 Scopus citations

Abstract

By applying methods of statistical physics Li and Sinai (J Eur Math Soc 10:267–313, 2008) proved that there are complex solutions of the Navier–Stokes equations in the whole space R³ which blow up at a finite time. We present a review of the results obtained so far, by theoretical work and computer simulations, for the singular complex solutions, and compare with the behavior of related real solutions. We also discuss the possible application of the techniques introduced in (J Eur Math Soc 10:267–313, 2008) to the study of the real ones.

Original language	English (US)
Journal	Journal of Statistical Physics
Volume	167
Issue number	1
DOIs	https://doi.org/10.1007/s10955-017-1730-1
State	Published - Apr 1 2017

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

Keywords

Blow-up
Global regularity
Navier–Stokes equations

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10.1007/s10955-017-1730-1

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abstract = "By applying methods of statistical physics Li and Sinai (J Eur Math Soc 10:267–313, 2008) proved that there are complex solutions of the Navier–Stokes equations in the whole space R3 which blow up at a finite time. We present a review of the results obtained so far, by theoretical work and computer simulations, for the singular complex solutions, and compare with the behavior of related real solutions. We also discuss the possible application of the techniques introduced in (J Eur Math Soc 10:267–313, 2008) to the study of the real ones.",

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N2 - By applying methods of statistical physics Li and Sinai (J Eur Math Soc 10:267–313, 2008) proved that there are complex solutions of the Navier–Stokes equations in the whole space R3 which blow up at a finite time. We present a review of the results obtained so far, by theoretical work and computer simulations, for the singular complex solutions, and compare with the behavior of related real solutions. We also discuss the possible application of the techniques introduced in (J Eur Math Soc 10:267–313, 2008) to the study of the real ones.

AB - By applying methods of statistical physics Li and Sinai (J Eur Math Soc 10:267–313, 2008) proved that there are complex solutions of the Navier–Stokes equations in the whole space R3 which blow up at a finite time. We present a review of the results obtained so far, by theoretical work and computer simulations, for the singular complex solutions, and compare with the behavior of related real solutions. We also discuss the possible application of the techniques introduced in (J Eur Math Soc 10:267–313, 2008) to the study of the real ones.

KW - Blow-up

KW - Global regularity

KW - Navier–Stokes equations

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Complex Singular Solutions of the 3-d Navier–Stokes Equations and Related Real Solutions

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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