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- W2626517294 abstract "This paper is devoted to the analysis of blow-up solutions for the nonlinear Schr{o}dinger equation with combined power-type nonlinearities [ iu_{t}+Delta u=lambda_1|u|^{p_1}u+lambda_2|u|^{p_2}u. ] When $p_1=frac{4}{N}$ and $0<p_2<frac{4}{N}$, we prove the existence of blow-up solutions and find the sharp threshold mass of blow-up and global existence for this equation. This is a complement to the result of Tao et al. (Comm. Partial Differential Equations 32: 1281-1343, 2007). Moreover, we investigate the dynamical properties of blow-up solutions, including $L^2$-concentration, blow-up rates and limiting profile. When $frac{4}{N}<p_1<frac{4}{N-2}$($4<p_1<infty$ if $N=1$, $2<p_1<infty$ if $N=2$), we prove that the blow-up solution with bounded $dot{H}^{s_c}$-norm must concentrate at least a fixed amount of the $dot{H}^{s_c}$-norm and, also, its $L^{p_c}$-norm must concentrate at least a fixed $L^{p_c}$-norm." @default.
- W2626517294 created "2017-06-23" @default.
- W2626517294 creator A5006033237 @default.
- W2626517294 date "2018-03-30" @default.
- W2626517294 modified "2023-09-27" @default.
- W2626517294 title "On the blow-up solutions for the nonlinear Schr{o}dinger equation with combined power-type nonlinearities" @default.
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- W2626517294 doi "https://doi.org/10.48550/arxiv.1803.11343" @default.
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