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- W2949984559 abstract "The aim of this paper is to show the small data scattering for 2D ICQNLS: $$iu_t=-Delta u + K_1(x)|u|^2u+K_2(x)|u|^4u.$$ Under the assumption that $left| partial^j K_l right| lesssim |x|^{b_l -j}$ for $j=0, 1, 2, l=1, 2$ and $0 le b_l le l - frac23$, we prove the small data scattering in an angularly regular Sobolev space $H_theta^{1,1}$. We use the decaying property of angularly regular functions, which are defined as functions in Sobolev space $H_theta^{1, 1} subset H^1$ with angular regularity such that $|partial_theta f|_{H^1} < infty$, and also use the recently developed angularly averaged Strichartz estimates cite{stri2, cholee, ghn}. In addition, we suggest a sufficient condition for non-existence of scattering." @default.
- W2949984559 created "2019-06-27" @default.
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- W2949984559 date "2019-04-24" @default.
- W2949984559 modified "2023-09-26" @default.
- W2949984559 title "Small data scattering of the inhomogeneous cubic-quintic NLS in 2 dimensions" @default.
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- W2949984559 doi "https://doi.org/10.48550/arxiv.1904.11073" @default.
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