Unconditional uniqueness of solution for H˙sc\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\dot H^{s_c }$$\end{document} critical 4th order NLS in high dimensions

In this paper, we study the unconditional uniqueness of solution for the Cauchy problem of H˙sc(0⩽sc<2)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\dot H^{s_c } (0 \leqslant s_c < 2)$$\end{document} critical nonlinear fourth-order Schrödinger equations i∂tu+Δ2u−ϵu = λ|u|αu. By employing paraproduct estimates and Strichartz estimates, we prove that unconditional uniqueness of solution holds in Ct(I;H˙sc(Rd))\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_t (I;\dot H^{s_c } (\mathbb{R}^d ))$$\end{document} for d ≥ 11 and min{1−,8d−4}⩾α>−(d−4)+(d−4)2+644\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\min \left\{ {1^ - ,\tfrac{8} {{d - 4}}} \right\} \geqslant \alpha > \frac{{ - (d - 4) + \sqrt {(d - 4)^2 + 64} }} {4}$$\end{document}.