Unconditional uniqueness of solution for H.sc critical 4th order NLS in high dimensions

Authors
Lu, Chao Lu, Jing
Citation
Lu, Chao et Lu, Jing, Unconditional uniqueness of solution for H.sc critical 4th order NLS in high dimensions, Acta mathematica Sinica. English series (Print) , 34(6), 2018, pp. 1028-1036
Journal title
Acta mathematica Sinica. English series (Print) → ACNP
ISSN journal
14398516
Volume
34
Issue
6
Year of publication
2018
Pages
1028 - 1036
Database
ACNP
SICI code
Abstract
In this paper, we study the unconditional uniqueness of solution for the Cauchy problem of H.sc(0.sc<2) critical nonlinear fourth-order Schrödinger equations i. t u+.2u..u = .|u|.u. By employing paraproduct estimates and Strichartz estimates, we prove that unconditional uniqueness of solution holds in Ct(I;H.sc(Rd)) for d . 11 and min{1.,8d.4}..>.(d.4)+(d.4)2+64.4.