arXiv subjects

Yingzhi Du

Publications and source records attributed to Yingzhi Du.

3 recordsLinked to original sources

arXiv2026

Global Existence of Strong and Weak Solutions to the 2D Compressible Navier-Stokes-Poisson System in Bounded Domains with Large Data and Vacuum

We study the two-dimensional compressible Navier-Stokes-Poisson system in a general simply connected bounded domain with Navier-slip boundary conditions and a positive, possibly non-flat, doping profile. We establish the global existence of a unique strong solution and of a global weak solution for arbitrarily large initial data allowing vacuum when the shear viscosity is a positive constant and the bulk one proportional to a power of the density with the power bigger than 4/3. The main difficulties arise from the interaction between the Poisson force and the general boundary geometry. To overcome them, we introduce a modified material derivative and derive quantitative $L^p$ estimates for the density by means of a Neumann duality argument together with a harmonic correction generated by the Navier-slip boundary condition. We further obtain a pointwise representation of the effective viscous flux by pulling back the Neumann Green function on the unit disk through a conformal mapping. The resulting commutator estimates, combined with elliptic estimates for the Poisson equation, yield a uniform-in-time upper bound for the density and allow us to close the higher-order a priori estimates. Finally, the global weak solution is constructed through a charge-preserving approximation and compactness argument.

math.AP↗

arXiv2024

Stability of steady states of the 3-D Navier-Stokes-Poisson equations with non-flat doping profile in exterior domains

This paper concerns an initial boundary value problem of compressible Navier-Stokes-Poisson equations with the non-flat doping profile in a 3-D exterior domain.The global existence of strong solutions near a steady state for compressible Navier-Stokes-Poisson equations with the general Navier-slip boundary conditions is established. For our setting, not only a steady state should be constructed in the exterior domain by the sub and super solution method, but also some new techniques should be adopted to obtain a priori estimates, especially some refined elliptic estimates and the estimates on the boundary.

math.AP↗

arXiv2024

Uniform Regularity for Incompressible MHD Equations in a Bounded Domain with Curved Boundary in 3D

For the initial boundary problem of the incompressible MHD equations in a bounded domain with general curved boundary in 3D with the general Navier-slip boundary conditions for the velocity field and the perfect conducting condition for the magnetic field, we establish the uniform regularity of conormal Sobolev norms and Lipschitz norms to addressing the anisotropic regularity of tangential and normal directions, which enable us to prove the vanishing dissipation limit as the viscosity and the magnetic diffusion coefficients tend to zero. We overcome the difficulties caused by the intricate interaction of boundary curvature, velocity field, and magnetic fields and resolve the issue caused by the problem that the viscosity and the magnetic diffusion coefficients are not required to be equal.

math.AP↗