Lower bounds of the lifespan of small data solutions to the nonlinear Schrödinger equations

Sunagawa, Hideaki

Osaka J. Math., Tome 43 (2006) no. 2, p. 771-789 / Harvested from Project Euclid

Résumé

Let $T_{\varepsilon}$ be the lifespan of solutions to the initial value problem for the one dimensional, derivative nonlinear Schrödinger equations with small initial data of size $O(\varepsilon)$. If the nonlinear term is cubic and gauge invariant, it is known that $\liminf_{\varepsilon \to +0} \varepsilon^{2} \log T_\varepsilon$ is positive. In this paper we obtain a sharp estimate of this lower limit, which is explicitly computed from the initial data and the nonlinear term.

Publié le : 2006-12-14
Classification: 35Q55, 35B40

@article{1165850035,
     author = {Sunagawa, Hideaki},
     title = {Lower bounds of the lifespan of small data solutions to the nonlinear Schr\"odinger equations},
     journal = {Osaka J. Math.},
     volume = {43},
     number = {2},
     year = {2006},
     pages = { 771-789},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1165850035}
}

Sunagawa, Hideaki. Lower bounds of the lifespan of small data solutions to the nonlinear Schrödinger equations. Osaka J. Math., Tome 43 (2006) no. 2, pp.  771-789. http://gdmltest.u-ga.fr/item/1165850035/