Smoothing effects and local existence theory for the nonlinear Schrödinger equations with non-constants coefficients;Effets régularisants et existence locale pour l'équation de Schrödinger non linéaire à coefficients variables

Comptes Rendus de l'Academie des Sciences - Series I: Mathematics

Volumn 331, Issue 5, 2000, Pages 375-378

  T'Joen, Laurent ^a  

^a UNIVERSITÉ PARIS SACLAY   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034259391     PISSN: 07644442     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0764-4442(00)01664-5     Document Type: Article

References (9)

1. [1] Chihara H., Local existence for semilinear Schrödinger equations, Math. Japonica 42 (1) (1995) 35-52.
2. [2] Constantin P., Saut J.-C., Local smoothing properties of dispersive equations, J. Amer. Math. Soc. 1 (1988) 413-439.
3. [3] Doï S.-I., Remarks on the Cauchy problem for Schrödinger type equations, Comm. Partial Differ. Eq. 21 (1996) 163-178.
4. [4] Doï S.-I., Smoothing effects of Schrödinger evolution groups on Riemannian manifolds, Duke Math. J. 82 (3) (1996) 679-706.
5. [5] Hayashi N., Ozawa T., Remarks on nonlinear Schrödinger equations in one space dimension, Differ, and Integ. Eq. 7 (2) (1994) 453-461.
6. [6] Kenig C., Ponce G., Vega L., Small solutions to nonlinear Schrödinger equations, Ann. Inst. Henri-Poincaré 10 (1993) 255-288.
7. [7] Kenig C., Ponce G., Vega L., Smoothing effects and local existence theory for the generalized nonlinear Schrödinger equations, Invent. Math. 134 (3) (1998) 489-545.
8. [8] Sjölin P., Regularity of solutions to the Schrödinger equations, Duke Math. J. 55 (1987) 699-715.
9. [9] Vega L., The Schrödinger equation: pointwise convergence to the initial date, Proc. Amer. Math. Soc. 102 (1988) 874-878.