10 papers
Discontinuity of the Vlasov--Poisson Flow in
Ke Chen, In-Jee Jeong, Quoc-Hung Nguyen +1
We prove that solution maps of the Vlasov--Poisson equation are discontinuous at the zero initial datum in for every , in $\mathbb{R}^{d} \tim…
Failure of analyticity-radius growth in energy-canceling fluid models
Ke Chen, Haina Li, Quoc-Hung Nguyen +1
We prove that exact quadratic energy cancellation alone does not force growth of the spatial analyticity radius. On , we construct an explicit symmetric, translation-…
Well-posedness for the mean curvature flow on the half-space and on bounded domains
Ke Chen, Ruilin Hu, Quoc-Hung Nguyen
We study graphical mean curvature flow in arbitrary codimension over the half-space and over smooth bounded domains, subject to homogeneous Dirichlet boundary conditions. At the sc…
Schauder-type Estimates and Log-Critical Well-posedness for the Two-Phase Muskat Problem with Surface Tension
Ke Chen, Ruilin Hu, Quoc-Hung Nguyen
We prove short-time well-posedness for the Muskat problem with surface tension in the full two-phase setting, allowing different viscosities, arbitrary density contrast, and rigid…
Schauder-type Estimates and Well-posedness for Nonlocal Quasilinear Evolution Equations in Fluid Dynamics
Ke Chen, Ruilin Hu, Quoc-Hung Nguyen
We establish Schauder-type estimates for linear parabolic systems driven by variable-coefficient nonlocal pseudo-differential operators of order . These estimates are formulat…
Scaling-Critical Theory for the Boltzmann and Landau Equations
Ke Chen, Quoc-Hung Nguyen, Tong Yang
This paper develops a scaling-critical theory for the spatially inhomogeneous non-cutoff Boltzmann and Landau equations with very soft potentials. For sufficiently small initial pe…
Well-posedness of the Fractional Fokker-Planck Equation
Ke Chen, Ruilin Hu, Quoc-Hung Nguyen
In this paper, we employ a Schauder-type estimate method, as developed in \cite{CHN}, to establish critical well-posedness result for the Fractional Fokker-Planck Equation. This eq…
The Muskat problem with a large slope
Yiran Xu, Stephen Cameron, Ke Chen +2
In this paper, we establish local well-posedness results for the Muskat equation in any dimension using modulus of continuity techniques. By introducing a novel quantity \(β_σ(f_0'…
Well-posedness for local and nonlocal quasilinear evolution equations in fluids and geometry
Ke Chen, Ruilin Hu, Quoc-Hung Nguyen
We establish a Schauder-type estimate for general local and non-local linear parabolic system in where $Λ=(-Δ)^{…
Local well-posedness of the compressible Navier-Stokes system with rough data
Ke Chen, Ruilin Hu, Quoc-Hung Nguyen
This paper presents a new approach to the local well-posedness of the compressible Navier-Stokes systems with rough initial data. Our approach is based on establishing some sm…