Non-generic Blow-up Solutions for the Critical Focusing Nls in 1-d
نویسندگان
چکیده
which blows up for t = −ab . Fixing a ∼ 1, b ∼ −1, it is then a natural question to ask whether one may perturb the initial data of (1.2) at time t = 0 such that the corresponding solution exhibits the same type of blow-up behavior. More precisely, the solution should asymptotically behave like √ 1 T−te iΨ(t,x)φ( T−t ) for a bounded function μ(t) and suitable Schwartz function φ, with blow up time T . The recent work of Merle-Raphael [MeRa] has demonstrated that this is generically impossible, i. e. there are open sets of initial
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