6 papers
Global existence and convergence of a density heat flow for strictly subcritical Liouville systems
Zetao Cheng, Haoyu Li, Woongbae Park +1
We study a density heat flow associated with normalized Liouville systems on a closed connected Riemannian surface, and we show that this flow leads to the existence of solutions f…
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…
Balance-Guided Sparse Identification of Multiscale Nonlinear PDEs with Small-coefficient Terms
Zhenhua Dang, Lei Zhang, Long Wang +1
Data-driven discovery of governing equations has advanced significantly in recent years; however, existing methods often struggle in multiscale systems where dynamically significan…
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 \[ i\partial_tu+Δu=|x|^{-b}|u|^{\frac{4-2b}{d-2}}u, \qquad (t,x)\in\R\times\R^d, \] with initia…
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} -Δu_i=\sum_{j=1}^n a_{ij}ρ_j\Big(\frac{h_j e^{u_j}}{\int_Ωh_j e^{u_j}}-1\Big)\mbo…
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} -Δu_i=\sum_{j=1}^n a_{ij}ρ_j\Big(\frac{h_j e^{u_j}}{\int_Ωh_j e^{u_j}}-1\…