Abstract
We consider the focusing mass-critical NLS in high dimensions , with initial data having finite mass . It is well known that this problem admits unique (but not global) strong solutions in the Strichartz class , and also admits global (but not unique) weak solutions in . In this paper we introduce an intermediate class of solution, which we call a semi-Strichartz class solution, for which one does have global existence and uniqueness in dimensions . In dimensions and assuming spherical symmetry, we also show the equivalence of the Strichartz class and the strong solution class (and also of the semi-Strichartz class and the semi-strong solution class), thus establishing unconditional uniqueness results in the strong and semi-strong classes. With these assumptions we also characterise these solutions in terms of the continuity properties of the mass function .
Citation
Terence Tao. "Global existence and uniqueness results for weak solutions of the focusing mass-critical nonlinear Schrödinger equation." Anal. PDE 2 (1) 61 - 81, 2009. https://doi.org/10.2140/apde.2009.2.61
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