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Yongshuai Gao

Publications and source records attributed to Yongshuai Gao.

5 recordsLinked to original sources
arXiv2023

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 $0<Ω<\infty$, 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 $β\nearrowβ^*:=a^*+\sqrt{(a^*-a_1)(a^*-a_2)}$, where $0 0$ is the unique positive solution of $-Δu+u-u^3=0$ in $\mathbb{R}^2$.

math.AP↗
arXiv2023

Existence and Asymptotic Behavior of Minimizers for Rotating Bose-Einstein Condensations in Bounded Domains

This paper is concerned with the existence and mass concentration behavior of minimizers for rotating Bose-Einstein condensations (BECs) with attractive interactions in a bounded domain $\mathcal{D}\subset \mathbb{R}^2$. It is shown that, there exists a finite constant $a^*$, denoting mainly the critical number of bosons in the system, such that the least energy $e(a)$ admits minimizers if and only if $0<a<a^*$, no matter the trapping potential $V(x)$ rotates at any velocity $Ω\geq0$. This is quite different from the rotating BECs in the whole plane case, where the existence conclusions depend on the value of $Ω$ (cf. \cite[Theorem 1.1]{GLY}). Moreover, by establishing the refined estimates of the rotation term and the least energy, we also analyze the mass concentration behavior of minimizers in a harmonic potential as $a\nearrow a^*$.

math.AP↗
arXiv2022

Nonexistence of Vortices for Rotating Two-Component Focusing Bose Gases

This paper is concerned with ground states of two-component Bose gases confined in a harmonic trap $V(x)=x_1^2+Λ^2 x_2^2$ rotating at the velocity $Ω>0$, where $Λ\ge 1$ and $(x_1, x_2)\in R^2$. We focus on the case 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. It is shown that for any $0<Ω<Ω^*:=2$, ground states exist if and only if $0 0$ is the unique positive solution of $-Δw+ w-w^3=0$ in $R^2$. By developing the argument of refined expansions, we further prove the nonexistence of vortices for ground states as $β\nearrowβ^*$, where $0<Ω<Ω^*$ and $0<a_1,\, a_2<a^*$ are fixed.

math-ph↗
arXiv2021

Mass concentration and uniqueness of ground states for mass subcritical rotational nonlinear Schrödinger equations

This paper considers ground states of mass subcritical rotational nonlinear Schrödinger equation \begin{equation*} -Δu+V(x)u+iΩ(x^\perp\cdot\nabla u)=μu+ρ^{p-1}|u|^{p-1}u \,\ \text{in} \,\ \mathbb{R}^2, \end{equation*} where $V(x)$ is an external potential, $Ω>0$ characterizes the rotational velocity of the trap $V(x)$, $1 0$ describes the strength of the attractive interactions. It is shown that ground states of the above equation can be described equivalently by minimizers of the $L^2-$ constrained variational problem. We prove that minimizers exist for any $ρ\in(0,\infty)$ when $0<Ω<Ω^*$, where $0<Ω^*:=Ω^*(V)<\infty$ denotes the critical rotational velocity of $V(x)$. While $Ω>Ω^*$, there admits no minimizers for any $ρ\in(0,\infty)$. For fixed $0<Ω<Ω^*$, by using energy estimates and blow-up analysis, we also analyze the limit behavior of minimizers as $ρ\to\infty$. Finally, we prove that up to a constant phase, there exists a unique minimizer when $ρ>0$ is large enough and $Ω\in(0,Ω^*)$ is fixed.

math.AP↗