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

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

We consider complex-valued solutions of the three-dimensional Navier-Stokes system without external forcing on $R^3$. 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 t...

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Veröffentlicht in:Journal of the European Mathematical Society : JEMS 2008-01, Vol.10 (2), p.267-313
Hauptverfasser: Li, Dong, Sinai, Yakov
Format: Artikel
Sprache:eng
Schlagworte:
Fluid mechanics
Group theory and generalizations
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Zusammenfassung:We consider complex-valued solutions of the three-dimensional Navier-Stokes system without external forcing on $R^3$. 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.
ISSN:1435-9855
1435-9863
DOI:10.4171/JEMS/111