Acta Mathematica Sinica, English Series

, Volume 34, Issue 6, pp 1028–1036 | Cite as

Unconditional uniqueness of solution for \(\dot H^{s_c }\) critical 4th order NLS in high dimensions

Article

Abstract

In this paper, we study the unconditional uniqueness of solution for the Cauchy problem of \(\dot H^{s_c } (0 \leqslant s_c < 2)\) critical nonlinear fourth-order Schrödinger equations i t u2u−ϵu = λ|u| α u. By employing paraproduct estimates and Strichartz estimates, we prove that unconditional uniqueness of solution holds in \(C_t (I;\dot H^{s_c } (\mathbb{R}^d ))\) for d ≥ 11 and \(\min \left\{ {1^ - ,\tfrac{8} {{d - 4}}} \right\} \geqslant \alpha > \frac{{ - (d - 4) + \sqrt {(d - 4)^2 + 64} }} {4}\).

Keywords

Unconditional uniqueness paraproduct estimates Besov spaces fourth order nonlinear Schrödinger equation 

MR(2010) Subject Classification

35Q55 42B25 46E35 

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Copyright information

© Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.The Graduate School of China Academy of Engineering PhysicsBeijingP. R. China
  2. 2.School of Mathematical SciencesBeijing Normal UniversityBeijingP. R. China

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