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This article is cited in 8 scientific papers (total in 8 papers)
Research Papers
Nondispersive vanishing and blow up at infinity for the energy critical nonlinear Schrödinger equation in $\mathbb R^3$
C. Ortoleva, G. Perelman Université Paris-Est Créteil, Créteil Cedex, France
Abstract:
The energy critical focusing nonlinear Schrödinger equation $i\psi_t=-\Delta\psi-|\psi|^4\psi$ in $\mathbb R^3$ is considered; it is proved that, for any $\nu$ and $\alpha_0$ sufficiently small, there exist radial finite energy solutions of the form $\psi(x,t)=e^{i\alpha(t)}\lambda^{1/2}(t)W(\lambda(t)x)+e^{i\Delta t}\zeta^*+o_{\dot H^1}(1)$ as $t\to+\infty$, where $\alpha(t)=\alpha_0\ln t$, $\lambda(t)=t^\nu$, $W(x)=(1+\frac13|x|^2)^{-1/2}$ is the ground state, and $\zeta^*$ is arbitrary small in $\dot H^1$.
Keywords:
energy critical focusing nonlinear Schrödinger equation, Cauchy problem, ground state, blow up.
Received: 02.10.2012
Citation:
C. Ortoleva, G. Perelman, “Nondispersive vanishing and blow up at infinity for the energy critical nonlinear Schrödinger equation in $\mathbb R^3$”, Algebra i Analiz, 25:2 (2013), 162–192; St. Petersburg Math. J., 25:2 (2014), 271–294
Linking options:
https://www.mathnet.ru/eng/aa1328 https://www.mathnet.ru/eng/aa/v25/i2/p162
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Abstract page: | 496 | Full-text PDF : | 113 | References: | 68 | First page: | 30 |
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