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

• Autores: Dong Li, Yakov G. Sinai
• Localización: Journal of the European Mathematical Society, ISSN 1435-9855, Vol. 10, Nº 2, 2008, págs. 267-313
• Idioma: inglés
• DOI: 10.4171/jems/111
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• Resumen

  • 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.

    Keywords: Navier-Stokes system, renormalization group theory, fixed point, linearization near the fixed point, spectrum of the linearized group, Hermite polynomials