论文标题
平均电场方程的冒泡解决方案，紧凑的Riemann表面上具有可变强度
Bubbling solutions for mean field equations with variable intensities on compact Riemann surfaces
论文作者
论文摘要
对于不对称的SINH-POISSON问题，该问题是作为平衡湍流涡度的平均场方程，在流体动力湍流中具有可变的强度，我们解决了紧凑型Riemann表面上冒泡溶液的存在。通过使用lyapunov-schmidt减少，我们发现有足够的条件下，存在$ s $的$ m $不同点起泡的解决方案，即$ s $：$ m_1 $点，$ m_1 $点，在$ m-m_1 $点上，$ m-m_1 $点，$ m \ ge 1 $ 1 $和$ m_1 $ and $ m_1 \ in \ in \ in \ in \ {0,1，...在不同情况下的几个示例说明了我们在Sphere $ \ Mathbb s^2 $和Flat Twip Tworus $ \ Mathbb t $中的结果说明了我们的结果。
For an asymmetric sinh-Poisson problem arising as a mean field equation of equilibrium turbulence vortices with variable intensities of interest in hydrodynamic turbulence, we address the existence of bubbling solutions on compact Riemann surfaces. By using a Lyapunov-Schmidt reduction, we find sufficient conditions under which there exist bubbling solutions blowing up at $m$ different points of $S$: positively at $m_1$ points and negatively at $m-m_1$ points with $m\ge 1$ and $m_1\in\{0,1,...,m\}$. Several examples in different situations illustrate our results in the sphere $\mathbb S^2$ and flat two-torus $\mathbb T$ including non negative potentials with zero set non empty.
