Bourgain, Jean Refinements of Strichartz’ inequality and applications to \(2D-NLS\) with critical nonlinearity. (English) Zbl 0917.35126 Int. Math. Res. Not. 1998, No. 5, 253-283 (1998). It is shown that if the initial data is in \(H^s(\mathbb{R}^2)\) with \(s<1\), then the local solution extends to a global one for the defocusing case. The result is of interest because of the absence of conserved quantities between \(L^2\) and energy norms. The main tool is the refinement of the classical theory for the paraboloid (Strichartz’ inequalities) as developed previously. Reviewer: L.Vazquez (Madrid) Cited in 8 ReviewsCited in 205 Documents MSC: 35Q55 NLS equations (nonlinear Schrödinger equations) 35A05 General existence and uniqueness theorems (PDE) (MSC2000) Keywords:nonlinear Schrödinger equation; critical nonlinearity; a priori estimates; local solution; global; defocusing case × Cite Format Result Cite Review PDF Full Text: DOI