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Refinements of Strichartz’ inequality and applications to \(2D-NLS\) with critical nonlinearity. (English) Zbl 0917.35126

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)

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
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