Zeros of complex caloric functions and singularities of complex viscous Burgers equation

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Abstract

We show that the viscous Burgers equation ut + uux = uxx considered for complex valued functions u develops finite-time singularities from compactly supported smooth data. By means of the Cole-Hopf transformation, the singularities of u are related to zeros of complex-valued solutions v of the heat equation vt = vxx. We prove that such zeros are isolated if they are not present in the initial data.

Original languageEnglish (US)
Pages (from-to)205-217
Number of pages13
JournalJournal fur die Reine und Angewandte Mathematik
Issue number616
DOIs
StatePublished - Mar 1 2008

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