Axial symmetry and refined spike profiles of ground states for rotating two-component Bose gases

This paper considers ground states of two-component Bose gases confined in an anharmonic trap rotating at the velocity $0<\Omega <\infty$, where the intraspecies interaction $(-a_1,-a_2)$ and the interspecies interaction −β are both attractive, i.e., $a_1,a_2$ and β are all positive. We prove the axially symmetry and the refined spike profiles of ground states as $\beta \nearrow {\beta }^{⁎}:=a^{⁎}+\sqrt{(a^{⁎}-a_1)(a^{⁎}-a_2)}$, where $0<a_1,a_2<a^{⁎}:={\Vert Q\Vert }_2^2$ are fixed and $Q>0$ is the unique positive solution of $-\Delta u+u-u^3=0$ in $R^2$.