Global existence of solutions to the generalized Proudman-Johnson equation

Chen, Xinfu; Okamoto, Hisashi

Proc. Japan Acad. Ser. A Math. Sci., Tome 78 (2002) no. 10, p. 136-139 / Harvested from Project Euclid

Résumé

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 $-3 \le a \le 1$.

Publié le : 2002-09-14
Classification: Proudman-Johnson equation, global existence, 35K55, 35Q30, 76D03

@article{1148392636,
     author = {Chen, Xinfu and Okamoto, Hisashi},
     title = {Global existence of solutions to the generalized Proudman-Johnson equation},
     journal = {Proc. Japan Acad. Ser. A Math. Sci.},
     volume = {78},
     number = {10},
     year = {2002},
     pages = { 136-139},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1148392636}
}

Chen, Xinfu; Okamoto, Hisashi. Global existence of solutions to the generalized Proudman-Johnson equation. Proc. Japan Acad. Ser. A Math. Sci., Tome 78 (2002) no. 10, pp.  136-139. http://gdmltest.u-ga.fr/item/1148392636/