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• W2024449135 abstract "We consider the 2-dimensional focusing mass critical NLS with an inhomogeneous nonlinearity: $ipartial_tu+Delta u+k(x)|u|^{2}u=0$. From standard argument, there exists a threshold $M_k>0$ such that $H^1$ solutions with $|u|_{L^2} M_k$. In this paper, we consider the dynamics at threshold $|u_0|_{L^2}=M_k$ and give a necessary and sufficient condition on $k$ to ensure the existence of critical mass finite time blow up elements. Moreover, we give a complete classification in the energy class of the minimal finite time blow up elements at a non degenerate point, hence extending the pioneering work by Merle who treated the pseudo conformal invariant case $kequiv 1$." @default.
• W2024449135 created "2016-06-24" @default.
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• W2024449135 date "2011-05-01" @default.
• W2024449135 modified "2023-10-15" @default.
• W2024449135 title "Existence and uniqueness of minimal blow-up solutions to an inhomogeneous mass critical NLS" @default.
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• W2024449135 doi "https://doi.org/10.1090/s0894-0347-2010-00688-1" @default.
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