Xiaobao Zhu

collaborators

3 papers

math.AP2025

Critical mean field equations for equilibrium turbulence with sign-changing prescribed functions

Linlin Sun, Xiaobao Zhu

Let $(M, g)$ be a compact Riemann surface with unit area. We investigate the mean field equation for equilibrium turbulence: \begin{align} \begin{cases} -Îu = Ï_1\left(\frac{h_1e^…

math.AP2024

Existence results for Toda systems with sign-changing prescribed functions: Part II

Linlin Sun, Xiaobao Zhu

Let $(M, g)$ be a compact Riemann surface with area $1$ . We investigate the Toda system \begin{align} \begin{cases} -Îu_1 = 2Ï_1(h_1e^{u_1}-1) - Ï_2(h_2e^{u_2}-1),\\ -Îu_2 = 2Ï…

math.AP2024

Existence results for Toda systems with sign-changing prescribed functions: Part I

LinLin Sun, Xiaobao Zhu

Let $(M, g)$ be a compact Riemann surface with area $1$ , we shall study the Toda system $$ \begin{cases} -Îu_1 = 2Ï_1(h_1e^{u_1}-1) - Ï_2(h_2e^{u_2}-1),\\ -Îu_2 = 2Ï_2(h_2e^{u_…