A mass supercritical and Sobolev critical fractional Schrödinger system

We study the following coupled fractional Schrödinger system: $$ \bcs (-\De)^s u=\la_1 u+\mu_1|u|^{p-2}u+\beta r_1|u|^{r_1-2}u|v|^{r_2}\quad &\hbox{in}\;\mathbb{R}^N, \\ (-\De)^s v=\la_2 v+\mu_2|v|^{q-2}v+\beta r_2|u|^{r_1}|v|^{r_2-2}v\quad &\hbox{in}\;\mathbb{R}^N, \\ %\int_{\mathbb{R}^N} u^2=a\quad and\quad \int_{\mathbb{R}^N} v^2=b, \ecs $$ with prescribed mass \[ \int_{\mathbb{R}^N} u^2=a\quad \hbox{and}\quad \int_{\mathbb{R}^N} v^2=b. \] Here, $a, b>0$ are prescribed, $N>2s, s>\frac{1}{2}$, $2+\frac{4s}{N}0$ sufficiently large, a mountain pass-type normalized solution exists provided $2\leq N\leq 4s$ and $ 2+\frac{4s}{N}