MR2428826
Kunio HIDANO
Kunio HIDANO
Nonlinear Schrödinger Equations with Radially Symmetric Data of Critical Regularity
Funkcialaj Ekvacioj. Serio Internacia
51
2008
135--147
http://fe.math.kobe-u.ac.jp/FE/FullPapers/51-1/51_135.pdf
http://www.ams.org/mathscinet-getitem?mr=MR2428826
This paper is concerned with the global existence of small solutions to pure-power nonlinear Schrödinger equations subject to radially symmetric data with critical regularity. Under radial symmetry we focus our attention on the case where the power of nonlinearity is somewhat smaller than the pseudoconformal power and the initial data belong to the scale-invariant homogeneous Sobolev space. In spite of the negative-order differentiability of initial data the nonlinear Schrödinger equation has global in time solutions provided that the initial data have the small norm. The key ingredient in the proof of this result is an effective use of global weighted smoothing estimates specific to radially symmetric solutions.
Nonlinear Schrödinger equation, Radial solutions, Critical regularity.
35Q55, 35B65.
51-135
2008
Nonlinear Schrödinger Equations with Radially Symmetric Data of Critical Regularity
Kunio HIDANO
Kunio HIDANO
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