Complex singularities of solutions of some 1D hydrodynamic models

Dong Li; Ya G. Sinai

doi:10.1016/j.physd.2007.11.015

Complex singularities of solutions of some 1D hydrodynamic models

Dong Li, Ya G. Sinai

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

12 Scopus citations

Abstract

We study the complex singularities of solutions of some classes of 1D hydrodynamic models. The method is based on the renormalization group theory. We derive the equation for the corresponding fixed point and study the spectrum of the linearized map near this point. This information allows to describe the initial condition for which blow ups at finite time can occur. We should stress that our solutions having blow ups are complex-valued.

Original language	English (US)
Pages (from-to)	1945-1950
Number of pages	6
Journal	Physica D: Nonlinear Phenomena
Volume	237
Issue number	14-17
DOIs	https://doi.org/10.1016/j.physd.2007.11.015
State	Published - Aug 15 2008

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics
Condensed Matter Physics
Applied Mathematics

Keywords

Blow up
Fixed point
Renormalization group

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10.1016/j.physd.2007.11.015

Cite this

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title = "Complex singularities of solutions of some 1D hydrodynamic models",

abstract = "We study the complex singularities of solutions of some classes of 1D hydrodynamic models. The method is based on the renormalization group theory. We derive the equation for the corresponding fixed point and study the spectrum of the linearized map near this point. This information allows to describe the initial condition for which blow ups at finite time can occur. We should stress that our solutions having blow ups are complex-valued.",

keywords = "Blow up, Fixed point, Renormalization group",

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

note = "Funding Information: The authors thank the anonymous referees for their many useful remarks and suggestions. The first author is supported by the NSF Grant DMS 0111298. The second author is supported by the NSF Grant DMS 0600996.",

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doi = "10.1016/j.physd.2007.11.015",

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T1 - Complex singularities of solutions of some 1D hydrodynamic models

AU - Li, Dong

AU - Sinai, Ya G.

N1 - Funding Information: The authors thank the anonymous referees for their many useful remarks and suggestions. The first author is supported by the NSF Grant DMS 0111298. The second author is supported by the NSF Grant DMS 0600996.

PY - 2008/8/15

Y1 - 2008/8/15

N2 - We study the complex singularities of solutions of some classes of 1D hydrodynamic models. The method is based on the renormalization group theory. We derive the equation for the corresponding fixed point and study the spectrum of the linearized map near this point. This information allows to describe the initial condition for which blow ups at finite time can occur. We should stress that our solutions having blow ups are complex-valued.

AB - We study the complex singularities of solutions of some classes of 1D hydrodynamic models. The method is based on the renormalization group theory. We derive the equation for the corresponding fixed point and study the spectrum of the linearized map near this point. This information allows to describe the initial condition for which blow ups at finite time can occur. We should stress that our solutions having blow ups are complex-valued.

KW - Blow up

KW - Fixed point

KW - Renormalization group

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DO - 10.1016/j.physd.2007.11.015

M3 - Article

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SN - 0167-2789

VL - 237

SP - 1945

EP - 1950

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

IS - 14-17

ER -

Complex singularities of solutions of some 1D hydrodynamic models

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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