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 language||English (US)|
|Number of pages||13|
|Journal||Journal fur die Reine und Angewandte Mathematik|
|State||Published - Mar 2008|
Bibliographical noteFunding Information:
2) Supported in part by NSF Grant DMS-0457061.
1) Supported in part by NSF Grant DMS-0400702.