Regular and Chaotic Dynamics

, Volume 15, Issue 4–5, pp 521–531 | Cite as

Blowups of complex-valued solutions for some hydrodynamic models

Special Issue: Valery Vasilievich Kozlov-60

Abstract

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.

Key words

blowup renormalization group method 

MSC2000 numbers

35Q35 

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Copyright information

© Pleiades Publishing, Ltd. 2010

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of IowaIowa CityUSA
  2. 2.Mathematics DepartmentPrinceton UniversityPrincetonUSA
  3. 3.Landau Institute of Theoretical PhysicsMoscow Region, ChernogolovkaRussia

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