Blowups of complex-valued solutions for some hydrodynamic models

We study complex-valued blowups of solutions for several hydrodynamic models. For complex-valued initial conditions, smooth local solutions can have finite-time singularities since the energy inequality does not hold. By using some version of the renormalization group method, we derive the equations...

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Bibliographic Details
Published in:Regular & chaotic dynamics 2010, Vol.15 (4-5), p.521-531
Main Authors: Li, D., Sinai, Ya. G.
Format: Article
Language:English
Subjects:
Dynamical Systems and Ergodic Theory
Mathematics
Mathematics and Statistics
Special Issue: Valery Vasilievich Kozlov-60
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Summary:We study complex-valued blowups of solutions for several hydrodynamic models. For complex-valued initial conditions, smooth local solutions can have finite-time singularities since the energy inequality does not hold. By using some version of the renormalization group method, we derive the equations for corresponding fixed points and analyze the spectrum of the linearized operator. We describe the open set of initial conditions for which blowups at finite time can occur.
ISSN:1560-3547
1560-3547
1468-4845
DOI:10.1134/S1560354710040088