13 citations · 83 across the 18 of their papers we have counts for
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Nonlinear asymptotic stability and transition threshold for 2D Taylor-Couette flows in Sobolev spaces
Xinliang An, Taoran He, Te Li
In this paper, we investigate the stability of the 2-dimensional (2D) Taylor-Couette (TC) flow for the incompressible Navier-Stokes equations. The explicit form of velocity for 2D…
ill-posedness for 2D Elastic Wave system
Xinliang An, Haoyang Chen, Silu Yin
In this paper, we prove that for the 2D elastic wave equations, a physical system with multiple wave-speeds, its Cauchy problem fails to be locally well-posed in $H^{\frac{11}{4}}(…
The Cauchy problems for the 2D compressible Euler equations and ideal MHD system are ill-posed in
Xinliang An, Haoyang Chen, Silu Yin
In a fractional Sobolev space with , we prove the low-regularity ill-posedness for the 2D compressible Euler equations and the 2D ideal compressib…
Enhanced dissipation and nonlinear asymptotic stability of the Taylor-Couette flow for the 2D Navier-Stokes equations
Xinliang An, Taoran He, Te Li
In this paper, we study the nonlinear stability of a steady circular flow created between two rotating concentric cylinders. The dynamics of the viscous fluid are described by 2D N…
Low regularity ill-posedness and shock formation for 3D ideal compressible MHD
Xinliang An, Haoyang Chen, Silu Yin
The study of magnetohydrodynamics (MHD) significantly boosts the understanding and development of solar physics, planetary dynamics and controlled nuclear fusion. Dynamical propert…
A scale-critical trapped surface formation criterion for the Einstein-Maxwell system
Xinliang An, Nikolaos Athanasiou
In this study we show that, from arbitrarily dispersed initial data, both the concentration of electromagnetic fields and the focusing of gravitational waves could lead to the form…
Trapped surface formation for spherically symmetric Einstein-Maxwell-charged scalar field system with double null foliation
Xinliang An, Zhan Feng Lim
In this paper, under spherical symmetry we prove a trapped surface formation criterion for the Einstein-Maxwell-charged scalar field system. We generalize an approach introduced by…
Curvature blow-up rates in spherically symmetric gravitational collapse to a Schwarzschild black hole
Xinliang An, Dejan Gajic
We study the black hole interiors of spacetimes arising from gravitational collapse in the spherically symmetric Einstein-scalar field setting, and we investigate the precise blow-…
Polynomial Blow-up Upper Bounds for the Einstein-scalar field System Under Spherical Symmetry
Xinliang An, Ruixiang Zhang
For general gravitational collapse, inside the black-hole region, singularities may arise. In this article, we aim to answer how strong these singularities could be. We ana…
Low regularity ill-posedness for elastic waves driven by shock formation
Xinliang An, Haoyang Chen, Silu Yin
In this paper, we construct counterexamples to the local existence of low-regularity solutions to elastic wave equations in three spatial dimensions (3D). Inspired by the recent wo…
A Scale-Critical Trapped Surface Formation Criterion: A New Proof via Signature for Decay Rates
Xinliang An
For gravitational collapse, we observe a correspondence between region close to past null infinity and region close to central singularity. In line with this philosophy, we constru…
Fermi's Golden Rule and Scattering for Nonlinear Klein-Gordon Equations with Metastable States
Xinliang An, Avy Soffer
In this paper, we explore the metastable states of nonlinear Klein-Gordon equations with potentials. These states come from the instability of a bound state under a nonlinear Fermi…