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

Hideaki Sunagawa

doi:ojm/1165850035

December 2006 Lower bounds of the lifespan of small data solutions to the nonlinear Schrödinger equations

Hideaki Sunagawa

Osaka J. Math. 43(4): 771-789 (December 2006).

Abstract

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.

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Hideaki Sunagawa "Lower bounds of the lifespan of small data solutions to the nonlinear Schrödinger equations," Osaka Journal of Mathematics 43(4), 771-789, (December 2006). https://doi.org/

Published: December 2006

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