Global existence of solutions to the Proudman-Johnson equation
Chen, Xinfu ; Okamoto, Hisashi
Proc. Japan Acad. Ser. A Math. Sci., Tome 76 (2000) no. 10, p. 149-152 / Harvested from Project Euclid
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We show that there is no blow-up solutions, for positive viscosity constant $\nu$, to the equation $f_{xxt} - \nu f_{xxxx} + f f_{xxx} - f_xf_{xx} =0$, $x \in (0,1)$, $t > 0$ with (i) periodic boundary condition, or (ii) Dirichlet boundary condition $f = f_x = 0$ or (iii) Neumann boundary condition $f = f_{xx} = 0$ on the boundary $x = 0, 1$. Furthermore we show that every solution decays to the trivial steady state as $t$ goes to infinity.
Publié le : 2000-11-14
Classification:  Proudman-Johnson equation,  global existence,  35K55,  35Q30,  76D03 
@article{1148393431,
     author = {Chen, Xinfu and Okamoto, Hisashi},
     title = {Global existence of solutions to the Proudman-Johnson equation},
     journal = {Proc. Japan Acad. Ser. A Math. Sci.},
     volume = {76},
     number = {10},
     year = {2000},
     pages = { 149-152},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1148393431}
}

Chen, Xinfu; Okamoto, Hisashi. Global existence of solutions to the Proudman-Johnson equation. Proc. Japan Acad. Ser. A Math. Sci., Tome 76 (2000) no. 10, pp.  149-152. http://gdmltest.u-ga.fr/item/1148393431/