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Blowup dynamics for mass critical Half-wave equation in 2D
Vladimir Georgiev, Yuan Li
We consider the half-wave equation in two dimensions. For the initial data , , we obtain the non-radia…
On mass - critical NLS with local and non-local nonlinearities
Vladimir Georgiev, Yuan Li
We consider the following nonlinear Schrödinger equation with the double -critical nonlinearities \begin{align*} iu_t+Δu+|u|^\frac{4}{3}u+μ\left(|x|^{-2}*|u|^2\right)u=0\ \ \…
Partial regularity and Liouville theorems for stable solutions of anisotropic elliptic equations
Mostafa Fazly, Yuan Li
We study the quasilinear elliptic equation \begin{equation*} -Qu=e^u \ \ \text{in} \ \ Ω\subset \mathbb{R}^{N} \end{equation*} where the operator , known as Finsler-Laplacian (o…
Nondispersive solutions to the mass critical half-wave equation in two dimensions
Vladimir Georgiev, Yuan Li
We consider the half-wave equation with mass critical in two dimension \begin{eqnarray*} \begin{cases} iu_t=Du-|u|u,\,\,\, \\ u(0,x)=u_0(x), \end{cases} \end{eqnarray*} First, we p…
Boson Stars with Long-range Perturbations
Qingxuan Wang, Binhua Feng, Yuan Li
We consider the Boson star equation with long-range perturbation given by $$i\partial_t ψ=\sqrt{-\triangle+m^2}\,ψ+β(\frac{1}{|x|^α}\ast |ψ|^2)ψ-(\frac{1}{|x|}\ast |ψ|^2)ψ \ \ \tex…