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On global solutions for the Constantin-Lax-Majda equation with a generalized viscosity term

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Title: On global solutions for the Constantin-Lax-Majda equation with a generalized viscosity term
Authors: Sakajo, Takashi1 Browse this author →KAKEN DB
Authors(alt): 坂上, 貴之1
Issue Date: Jul-2003
Publisher: Institute of Physics
Journal Title: Nonlinearity
Volume: 16
Issue: 4
Start Page: 1319
End Page: 1328
Publisher DOI: 10.1088/0951-7715/16/4/307
Abstract: We consider a one-dimensional model for the three-dimensional vorticity equation of incompressible and viscous fluids. This model is obtained by adding a generalized viscous diffusion term to the Constantin-Lax-Majda equation, which was introduced as a model for the 3-D Euler equation[2]. It is shown in [6] that the solution of the model equation blows up in finite time for sufficiently small viscosity, however large diffusion term it may has. In the present article, we discuss the existence of a unique global solution for large viscosity.We investigate convergence of the solution and show that the solution blows up in finite time for sufficiently small viscosity coefficient regardless of the order of derivative of the viscosity term.
Description URI: http://www.iop.org/
Rights: Copyright © 2003 IOP Publishing Ltd.
Type: article (author version)
URI: http://hdl.handle.net/2115/5415
Appears in Collections:理学院・理学研究院 (Graduate School of Science / Faculty of Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)

Submitter: 坂上 貴之

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