Complex singularities of solutions of some 1D hydrodynamic models

Dong Li, Ya G. Sinai

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


We study the complex singularities of solutions of some classes of 1D hydrodynamic models. The method is based on the renormalization group theory. We derive the equation for the corresponding fixed point and study the spectrum of the linearized map near this point. This information allows to describe the initial condition for which blow ups at finite time can occur. We should stress that our solutions having blow ups are complex-valued.

Original languageEnglish (US)
Pages (from-to)1945-1950
Number of pages6
JournalPhysica D: Nonlinear Phenomena
Issue number14-17
StatePublished - Aug 15 2008

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics


  • Blow up
  • Fixed point
  • Renormalization group


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