Journal ArticleDOI
Monotonicity method for the complex Ginzburg–Landau equation, including smoothing effect
N. Okazawa,T. Yokota +1 more
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This article is published in Nonlinear Analysis-theory Methods & Applications.The article was published on 2001-08-01. It has received 18 citations till now. The article focuses on the topics: Landau theory & Ginzburg–Landau theory.read more
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Finite-Time Blowup for a Complex Ginzburg--Landau Equation
TL;DR: In this paper, it was shown that negative energy solutions of the complex Ginzburg-Landau equation can be solved in finite time, where α > 0 and α < 2.
Journal ArticleDOI
Finite-time blowup for a complex Ginzburg-Landau equation
TL;DR: It turns out that $T_{max}^\theta $ stays bounded as $\theta \to \pm \pi /2 $ in the case where the solution of the limiting nonlinear Schr\"odinger equation blows up in finite time.
Journal ArticleDOI
Uniqueness and Inviscid Limits of Solutions for the Complex Ginzburg-Landau Equation in a Two-Dimensional Domain
Takayoshi Ogawa,Tomomi Yokota +1 more
Journal ArticleDOI
Life-span of smooth solutions to the complex Ginzburg–Landau type equation on a torus
Tohru Ozawa,Y Yamazaki +1 more
TL;DR: An upper bound of the life-span of smooth solutions to the complex Ginzburg-Landau equation with periodic boundary condition in one space dimension is given explicitly in terms of an integral mean of the Cauchy data in the case where the interaction is focusing as mentioned in this paper.
Journal ArticleDOI
A Fujita-type blowup result and low energy scattering for a nonlinear Schr\"o\-din\-ger equation
TL;DR: In this article, the authors considered the nonlinear Schr\"o\-din\-ger equation and showed that small data can give rise to global, low energy scattering solutions in dimensions $H^1.
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Monotonicity Method Applied to the Complex Ginzburg–Landau and Related Equations
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The Cauchy problem in local spaces for the complex Ginzburg-Landau equation I: compactness methods
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