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

P. Poláčik; V. Šverák

doi:10.1515/CRELLE.2008.022

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

P. Poláčik, V. Šverák

Mathematics

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

Abstract

We show that the viscous Burgers equation u_t + uu_x = u_xx 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 v_t = v_xx. We prove that such zeros are isolated if they are not present in the initial data.

Original language	English (US)
Pages (from-to)	205-217
Number of pages	13
Journal	Journal fur die Reine und Angewandte Mathematik
Issue number	616
DOIs	https://doi.org/10.1515/CRELLE.2008.022
State	Published - Mar 2008

Bibliographical note

Funding Information:
2) Supported in part by NSF Grant DMS-0457061.

Funding Information:
1) Supported in part by NSF Grant DMS-0400702.

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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.",

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

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