Unconditional uniqueness of solution forH˙sccritical NLS in high dimensions

Abstract

In this paper, we study the unconditional uniqueness of solution for the Cauchy problem of Ḣsc (0 ≤ s c < 1) critical nonlinear Schrödinger equations (NLS). By employing paraproduct estimates and Strichartz estimates, we prove that unconditional uniqueness of solution holds in C t (I; Ḣsc (R d )) for d ≥ 6. This extends earlier results by Yin Yin Su Win and Y. Tsutsumi [19] and Cazenave [3].

Unconditional uniqueness results for the nonlinear Schrödinger equation

“…We henceforth consider only the nontrivial regime s < d/2. The first such result on R d is that of Kato [26,27], with subsequent extensions and improvements in dimension d ≥ 2 obtained in [7,14,15,21,31,38,43,44], we refer to these references for precise results. The inherent losses of derivatives in the Strichartz estimate do not allow one to adapt these arguments to compact domains.…”