Zeros of complex caloric functions and singularities of complex viscous Burgers equation
Analysis of PDEs
2007-05-23 v1
Abstract
We show that the 1d viscous Burgers equation considered for complex valued functions develops finite-time singularities from compactly supported smooth data. By means of the Cole-Hopf transformation, the singularities of the solutions are related to zeros of complex-valued solutions of the heat equation. We prove that such zeros are isolated if they are not present in the initial data.
Keywords
Cite
@article{arxiv.math/0612506,
title = {Zeros of complex caloric functions and singularities of complex viscous Burgers equation},
author = {Peter Polacik and Vladimir Sverak},
journal= {arXiv preprint arXiv:math/0612506},
year = {2007}
}
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16 pages