Blowups of complex-valued solutions for some hydrodynamic models

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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.

Original languageEnglish (US)
Pages (from-to)521-531
Number of pages11
JournalRegular and Chaotic Dynamics
Volume15
Issue number4
DOIs
StatePublished - 2010

All Science Journal Classification (ASJC) codes

  • Mathematics (miscellaneous)

Keywords

  • blowup
  • renormalization group method

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