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arXiv · 1210.0606

Small data blow-up for a system of nonlinear Schr\"odinger equations

Tohru Ozawa·Hideaki Sunagawa
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Abstract

We give examples of small data blow-up for a three-component system of quadratic nonlinear Schr\"odinger equations in one space dimension. Our construction of the blowing-up solution is based on the Hopf-Cole transformation, which allows us to reduce the problem to getting suitable growth estimates for a solution to the transformed system. Amplification in the reduced system is shown to have a close connection with the mass resonance.

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Tohru Ozawa, Hideaki Sunagawa. 2012-10-02. Small data blow-up for a system of nonlinear Schr\"odinger equations. https://arxiv.org/abs/1210.0606

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