Well-posedness and smoothing effect for generalized nonlinear Schrödinger equations

Pierre-Yves Bienaimé (1) , Abdesslam Boulkhemair (1)

1 LMJL - Laboratoire de Mathématiques Jean Leray

We improve the result obtained by one of the authors, [Bie], and establish the well posed-ness of the Cauchy problem for some nonlinear equations of Schrödinger type in the usual Sobolev space H s (R n) for s > n 2 + 2 instead of s > n 2 + 3 in [Bie]. We also improve the smoothing effect of the solution and obtain the optimal exponent.

Mots clés: smoothing effect; well posedness; Cauchy problem; nonlinear equations of Schrödinger type; paradifferential; pseudodifferential; operator; paralinearization

Domaines: Equations aux dérivées partielles [math.AP]; Analyse fonctionnelle [math.FA]

Pierre-Yves Bienaimé, Abdesslam Boulkhemair. Well-posedness and smoothing effect for generalized nonlinear Schrödinger equations. 2017. ⟨hal-01515658v2⟩