13 citations · 83 across the 18 of their papers we have counts for
20 papers
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…
Quantitative blow-up estimates for spacelike singularities in gravitational-collapse cosmological spacetimes
Xinliang An, Haoyang Chen, Taoran He
Under spherical symmetry, with double-null coordinates , we study the gravitational collapse of the Einstein--scalar field system with a positive cosmological constant. The…
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…
Anisotropic Dynamical Horizons Arising in Gravitational Collapse
Xinliang An, Qing Han
For the study of dimensional Einstein vacuum equations (EVEs), substantial progress has been made recently on the problem of trapped surface formation. However, very limited…
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…
Warped Product Space-times
Xinliang An, Willie Wai Yeung Wong
Many classical results in relativity theory concerning spherically symmetric space-times have easy generalizations to warped product space-times, with a two-dimensional Lorentzian…
Emergence of Apparent Horizon in Gravitational Collapse
Xinliang An
We solve Einstein vacuum equations in a spacetime region up to the "center" of gravitational collapse. Within this region, we construct a sequence of marginally outer trapped surfa…
Naked singularity and black hole formation in self-similar Einstein-scalar fields with exponential potentials
Xuefeng Zhang, Xinliang An
Motivated by cosmic censorship in general relativity and string theory, we extend Christodoulou's celebrated examples of naked singularity formation in the Einstein-massless scalar…
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…
Examples of naked singularity formation in higher-dimensional Einstein-vacuum spacetimes
Xinliang An, Xuefeng Zhang
The vacuum Einstein equations in 5+1 dimensions are shown to admit solutions describing naked singularity formation in gravitational collapse from nonsingular asymptotically locall…
Trapped surfaces in vacuum arising dynamically from mild incoming radiation
Xinliang An, Jonathan Luk
In this paper, we study the "minimal requirement" on the incoming radiation that guarantees a trapped surface to form in vacuum. First, we extend the region of existence in Christo…
Formation of Trapped Surfaces from Past Null Infinity
Xinliang An
In this paper, we extend the results of Klainerman and Rodnianski in \cite{KR:Trapped}, which were obtained for a finite region, by showing similar results from past null infinity.…