1 citations · 1 across the 9 of their papers we have counts for
9 papers
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…
Solutions of the 3D inhomogeneous incompressible Navier-Stokes system with initial velocity in
Ruilin Hu, Quoc-Hung Nguyen, Feng Shao +3
In this paper, we establish local existence of strong solutions for the three-dimensional inhomogeneous incompressible Navier-Stokes equations with initial data lying i…
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…
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'…
Quantitative bounds for bounded solutions to the Navier-Stokes equations in endpoint critical Besov spaces
Ruilin Hu, Phuoc-Tai Nguyen, Quoc-Hung Nguyen +1
Building on Tao's quantitative regularity theory and triple-logarithmic blow-up estimate in in \cite{Tao_20}, we consider classical solutions of the three-dimensional…
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…