The local and global well-posedness for the Cauchy problem for a class of nonlinear Schrödinger equations is studied. The global well-posedness of the problem is proved in the Sobolev space Hs = Hs(Rn) of fractional order s > n/2 under the following assumptions. (1) Concerning the Cauchy data φ ∈ Hs: ∥φ; L2∥ is relatively small with respect to ∥φ; Hσ∥ for any fixed σ with n/2 < σ ≤ s. (2) Concerning the nonlinearity f: f(u) behaves as a conformal power u1+4/n near zero and has an arbitrary growth rate at infinity.
|ジャーナル||Journal d'Analyse Mathematique|
|出版ステータス||Published - 2000 1月 1|
ASJC Scopus subject areas
- 数学 (全般)