arXiv subjects

Zhengguang Guo

Publications and source records attributed to Zhengguang Guo.

4 recordsLinked to original sources

arXiv2026

Steady compressible Navier-Stokes-Fourier system with general temperature dependent viscosities and hard sphere pressure law

We study the existence theory for steady compressible Navier-Stokes-Fourier system in a three dimensional bounded domain for the case of viscosities depending on the temperature in the form $(1+\vartheta)^α$ for $0\leq α\leq 1$ and the hard sphere pressure $p(\varrho,\vartheta) = \vartheta\varrho h(\varrho)$, $h(\varrho)$ is increasing and singular at $\varrho = a > 0$. This paper considers both the heat-flux and Dirichlet boundary conditions for the temperature and Dirichlet boundary conditions for the velocity. The key point to controlling the pressure is based on some estimates of the Bogovskii operator.

math.AP↗

arXiv2024

Extension of Hamel paradox for the 2D exterior Navier-Stokes problem

In this paper, we continue the analysis of the stationary exterior Navier-Stokes problem with interior boundary data and vanishing condition at infinity. We first show an existence result that extends a previous contribution of the second author by considering boundary data prescribing a non-trivial flux on the internal boundary. We obtain in particular that the non-uniqueness result of G. Hamel extends to an open set of internal boundary data. We then show that one way to recover uniqueness of a solution is to complement the perturbation of velocity field with a decay condition at infinity for small circulation through the interior boundary. Our method is based on a fine analysis of the linearized Navier-Stokes system around potential flows in the exterior domain.

math.AP↗

arXiv2022

On the uniqueness and non-uniqueness of the steady planar Navier-Stokes equations in an exterior domain

In this paper we investigate the uniqueness of solutions of the steady planar Navier-Stokes equations with different boundary conditions in the exterior domain. For a class of incompressible flow with constant vorticity, we prove the uniqueness of the solution under the enhanced Navier boundary conditions. At the same time, some counterexamples are given to show that the uniqueness of the solution fails under the Navier boundary conditions. For the general incompressible flow with Dirichlet boundary condition, we prove various sufficient conditions for the uniqueness of the solution.

math.AP↗

arXiv2020

Global strong solutions to the inhomogeneous incompressible Navier-Stokes system in the exterior of a cylinder

In this paper, the global strong axisymmetric solutions for the inhomogeneous incompressible Navier-Stokes system are established in the exterior of a cylinder subject to the Dirichlet boundary conditions. Moreover, the vacuum is allowed in these solutions. One of the key ingredients of the analysis is to obtain the ${L^{2}(s,T;L^{\infty}(Ω))}$ bound for the velocity field, where the axisymmetry of the solutions plays an important role.

math.AP↗