3 papers
math.AP2026
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…
math.AP2025
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…
math.AP2024
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'…