Proceedings of the Japan Academy, Series A, Mathematical Sciences

Global existence of solutions to the generalized Proudman-Johnson equation

Xinfu Chen and Hisashi Okamoto

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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 $-3 \le a \le 1$.

Article information

Proc. Japan Acad. Ser. A Math. Sci., Volume 78, Number 7 (2002), 136-139.

First available in Project Euclid: 23 May 2006

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Primary: 35K55: Nonlinear parabolic equations 35Q30: Navier-Stokes equations [See also 76D05, 76D07, 76N10] 76D03: Existence, uniqueness, and regularity theory [See also 35Q30]

Proudman-Johnson equation global existence


Chen, Xinfu; Okamoto, Hisashi. Global existence of solutions to the generalized Proudman-Johnson equation. Proc. Japan Acad. Ser. A Math. Sci. 78 (2002), no. 7, 136--139. doi:10.3792/pjaa.78.136.

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