4 papers · 1 filter
Local Uniqueness and Non-degeneracy of Blow Up Solutions To A Chern-Simons System
Zetao Cheng, Haoyu Li, Lei Zhang
In this paper, we study blowup solutions of an important class of Chern-Simons systems. We first show that when blowup of mean-field type occurs, the corresponding blowup solution…
Global well-posedness and scattering for defocusing energy-critical inhomogeneous NLS in dimensions
Bo Yang, Lei Zhang, Bin Liu
We study the defocusing energy-critical inhomogeneous nonlinear Schrödinger equation \[ i\partial_tu+Îu=|x|^{-b}|u|^{\frac{4-2b}{d-2}}u, \qquad (t,x)\in\R\times\R^d, \] with init…
Construction of blowup solutions for Liouville systems
Zetao Cheng, Haoyu Li, Lei Zhang
We study the following Liouville system defined on a flat torus \begin{equation} \left\{ \begin{array}{lr} -Îu_i=\sum_{j=1}^n a_{ij}Ï_j\Big(\frac{h_j e^{u_j}}{\int_Ωh_j e^{u_j}}…
Local uniqueness and non-degeneracy of blowup solutions for regular Liouville systems
Zetao Cheng, Haoyu Li, Lei Zhang
We study the following Liouville system defined on a compact Riemann surface , \begin{equation} -Îu_i=\sum_{j=1}^n a_{ij}Ï_j\Big(\frac{h_j e^{u_j}}{\int_Ωh_j e^{u_j}}-1\Big)\…