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 $-3 \le a \le 1$.
Citation
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
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