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u\rightarrow (2\pi)^{-1/2}(\ii t)^{-1/2}e^{\ii x^2/(2t)}\, W\!\Big(\frac{x}{t}\Big)\exp(-\ii\la|W(x/t)|^2\log t). \end{equation*} Crucially, we design a contraction map, so that we can run the analysis in the spirit of Kato--Pusateri \cite{KP} for $w$ with a forcing term depending {\it only} on the final data $W$. This scheme is easy to adapt to solving final state problems with a complete theory for the forward problems.
From: Gong Chen [view email]
[v1]
Thu, 21 May 2026 21:54:40 UTC (17 KB)
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