Remarks on Blowing-Up of Solutions for Some Nonlinear Schrödinger Equations

KURATA, Kazuhiro; OGAWA, Takayoshi

Tokyo J. of Math., Tome 13 (1990) no. 2, p. 399-419 / Harvested from Project Euclid

Résumé

We study the blowing-up conditions of solutions for nonlinear Schrödinger equations with interaction which does not satisfy known Glassey's condition [4]. We also give some remarks on the blowing-up conditions on an exterior domain with a star-shaped complement under the Dirichlet boundary condition and on a complement of a ball under the Neumann boundary condition. Finally, we show global existence of solutions for the equation: $i\dfrac{\partial u}{\partial t}=\Delta u+\left(\dfrac{1}{|x|^2}*|u|^2\right)u$.

Publié le : 1990-12-15
Classification:

@article{1270132270,
     author = {KURATA, Kazuhiro and OGAWA, Takayoshi},
     title = {Remarks on Blowing-Up of Solutions for Some Nonlinear Schr\"odinger Equations},
     journal = {Tokyo J. of Math.},
     volume = {13},
     number = {2},
     year = {1990},
     pages = { 399-419},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1270132270}
}

KURATA, Kazuhiro; OGAWA, Takayoshi. Remarks on Blowing-Up of Solutions for Some Nonlinear Schrödinger Equations. Tokyo J. of Math., Tome 13 (1990) no. 2, pp.  399-419. http://gdmltest.u-ga.fr/item/1270132270/