10 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…
Local Well-Posedness for Vlasov--Poisson with Initial Density and Fractional Velocity Regularity
Quoc-Hung Nguyen
We prove a local well-posedness criterion for the Vlasov--Poisson system on , , under an anisotropic assumption on the initial distribution. The datum h…
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…
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…
Wolff potentials and nonlocal equations of Lane-Emden type
Quoc-Hung Nguyen, Jihoon Ok, Kyeong Song
We consider nonlocal equations of the type \[ (-Î_{p})^{s}u = μ\quad \text{in}\;\; Ω, \] where is either a bounded domain or the whole $\mathbb{R}^{n}…
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…