Kenig, Carlos E. Local well posedness of nonlinear Schrödinger equations. (English) Zbl 0874.35112 Journ. Équ. Dériv. Partielles, St.-Jean-de-Monts 1995, Exp. No. 10, 6 p. (1995). In this note I describe some recent work, done jointly with Gustav Ponce and Luis Vega, on nonlinear Schrödinger equations of the form \[ i{\partial u\over\partial t}+ \Delta u+F(u,\overline u,\nabla_xu,\nabla_x\overline u)=0,\quad u(x,0)=u_0(x), \] where \(x\in \mathbb{R}^n\), \(t\in [0,T]\). Here \(F:\mathbb{C}^{2n+2} \to\mathbb{C}\) is a polynomial having no constant or linear terms. We are interested in establishing local well posedness results, and global well posedness results, with data in Sobolev spaces. MSC: 35Q55 NLS equations (nonlinear Schrödinger equations) 35A05 General existence and uniqueness theorems (PDE) (MSC2000) 35A07 Local existence and uniqueness theorems (PDE) (MSC2000) Keywords:nonlinear Schrödinger equations; local well posedness; global well posedness PDFBibTeX XMLCite \textit{C. E. Kenig}, Journ. Équ. Dériv. Partielles, St.-Jean-de-Monts 1995, Exp. No. 10, 6~p. (1995; Zbl 0874.35112) Full Text: Numdam EuDML