Singularities of complex-valued solutions of the two-dimensional Burgers system

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Abstract

We consider the two-dimensional viscous Burgers system without external forcing. For complex-valued solutions, due to the loss of maximum principle and energy estimates, smooth solutions can develop finite-time singularities. We construct an open set of six-parameter families of initial conditions such that the corresponding solutions exhibit blowups in finite time.

Original languageEnglish (US)
Article number007091JMP
JournalJournal of Mathematical Physics
Volume51
Issue number1
DOIs
StatePublished - Jan 1 2010

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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