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On blowup for the pseudo-conformally invariant nonlinear Schrödinger equation II

✍ Scribed by Hayato Nawa; Masayoshi Tsutsumi


Publisher
John Wiley and Sons
Year
1998
Tongue
English
Weight
96 KB
Volume
51
Category
Article
ISSN
0010-3640

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✦ Synopsis


We study the δ-measure-like blowup of solutions to the pseudo-conformally invariant nonlinear Schrödinger equation

For N = 1 or N ≥ 2 and u0 radially symmetric, we prove that if the blowup solution u(t) satisfies |u(t, x)| 2 dx u0 2 δ0(dx) in the sense of measures as t ↑ Tm (i.e., weakly * in B , which is the dual of

where Tm > 0 is the maximal existence time and δ0 is the Dirac measure at 0 ∈ R N , then u0 must satisfy

and we have lim t→Tm |x|u(t) L 2 (R N ) = 0 .


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