Hokkaido Mathematical Journal

WIN Yin Yin Su, TSUTSUMI Yoshio,

Unconditional uniqueness of solution for the Cauchy problem of the nonlinear Schrödinger equation.

Hokkaido Mathematical Journal, 37 (2008) pp.839-859

Fulltext

PDF

Abstract

We study the unconditional uniqueness of solution for the Cauchy problem of the nonlinear Schrödinger equation. We show the uniqueness of solution in C([0, T]; H^s) for the critical case or L^\infty(0, T; H^s) for the subcritical case under certain assumptions on spatial dimensions and power of nonlinearity. We do not assume the solution belongs to any auxiliary spaces associated with the Strichartz estimate. For that purpose, we also prove the estimate of product between functions and distributions and the continuity of mapping: u \to |u| on the homogeneous Sobolev or Besove space.

MSC(Primary)35Q55
MSC(Secondary)42B35
Uncontrolled Keywordsunconditional uniqueness, nonlinear Schrödinger equation, homogeneous Besov space.