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arXiv · 1912.12794

Lifespan of solutions to nonlinear Schrödinger equations with general homogeneous nonlinearity of the critical order

Hayato Miyazaki·Motohiro Sobajima
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Abstract

This paper is concerned with the upper bound of the lifespan of solutions to nonlinear Schrödinger equations with general homogeneous nonlinearity of the critical order. In [8], Masaki and the first author obtain the upper bound of the lifespan of solutions to our equation via a test function method introduced by [16, 17]. Their nonlinearity contains a non-oscillating term $|u|^{1+2/d}$ which causes difficultly for constructing an even small data global solution. The non-oscillating term corresponds to the $L^1$-scaling critical. In this paper, it turns out that the upper bound can be refined by employing an unified test function by Ikeda and the second author [5].

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Hayato Miyazaki, Motohiro Sobajima. 2020-03-15. Lifespan of solutions to nonlinear Schrödinger equations with general homogeneous nonlinearity of the critical order. https://doi.org/10.1007/978-3-030-58215-9_7

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