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Sept. 2002 Global existence of solutions to the generalized Proudman-Johnson equation
Xinfu Chen, Hisashi Okamoto
Proc. Japan Acad. Ser. A Math. Sci. 78(7): 136-139 (Sept. 2002). DOI: 10.3792/pjaa.78.136

Abstract

We consider the equation $f_{xxt} + f f_{xxx} - a f_x f_{xx} = \nu f_{xxxx}$, $x \in (0,1)$, $t > 0 $, where $a \in \mathbf{R}$ is a constant, with the periodic boundary condition. We show that any solution exists globally in time if $-3 \le a \le 1$.

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Xinfu Chen. Hisashi Okamoto. "Global existence of solutions to the generalized Proudman-Johnson equation." Proc. Japan Acad. Ser. A Math. Sci. 78 (7) 136 - 139, Sept. 2002. https://doi.org/10.3792/pjaa.78.136

Information

Published: Sept. 2002
First available in Project Euclid: 23 May 2006

zbMATH: 1020.35002
MathSciNet: MR1930218
Digital Object Identifier: 10.3792/pjaa.78.136

Subjects:
Primary: 35K55 , 35Q30 , 76D03

Keywords: global existence , Proudman-Johnson equation

Rights: Copyright © 2002 The Japan Academy

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Vol.78 • No. 7 • Sept. 2002
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