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

Dong Li; Yakov G. Sinai

doi:10.1063/1.3276099

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

Dong Li, Yakov G. Sinai

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9 Scopus citations

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 language	English (US)
Article number	007091JMP
Journal	Journal of Mathematical Physics
Volume	51
Issue number	1
DOIs	https://doi.org/10.1063/1.3276099
State	Published - Jan 2010

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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10.1063/1.3276099

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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.",

author = "Dong Li and Sinai, {Yakov G.}",

note = "Funding Information: The first author is supported in part by NSF Grant No. DMS 0908032 and a start-up funding from the Mathematics Department of University of Iowa. The second author acknowledges the financial support from NSF Grant No. DMS 0600996.",

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

Abstract

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