On the asymptotic behavior of large radial data for a focusing non-linear Schrödinger equation
نویسندگان
چکیده
منابع مشابه
On the Asymptotic Behavior of Large Radial Data for a Focusing Non-linear Schrödinger Equation
We study the asymptotic behavior of large data radial solutions to the focusing Schrödinger equation iut+∆u = −|u|2u in R, assuming globally bounded H1(R) norm (i.e. no blowup in the energy space). We show that as t → ±∞, these solutions split into the sum of three terms: a radiation term that evolves according to the linear Schrödinger equation, a smooth function localized near the origin, and...
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. A P ] 8 O ct 2 00 6 GLOBAL WELL - POSEDNESS , SCATTERING AND BLOW - UP FOR THE ENERGY - CRITICAL , FOCUSING , NON - LINEAR SCHRÖDINGER EQUATION IN THE RADIAL CASE
∞(i.e. the solution scatters in Ḣ(R )). See section 2 of this paper for a review of these results. In the defocusing case, Bourgain ([5], [6]) proved that, for N = 3, 4 and u0 radial, this also holds for ||u0||Ḣ1 < +∞, and that for more regular u0, the solution preserves the smoothness for all time. (Another proof of this last fact is due to Grillakis [13] for N = 3). Bourgain’s result was then...
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ژورنال
عنوان ژورنال: Dynamics of Partial Differential Equations
سال: 2004
ISSN: 1548-159X,2163-7873
DOI: 10.4310/dpde.2004.v1.n1.a1