arXiv subjects

Qinghao Lei

Publications and source records attributed to Qinghao Lei.

7 recordsLinked to original sources

arXiv2026

Global Existence and Incompressible Limit for the Two-Dimensional Compressible Navier-Stokes Equations in a Half-Space with Large Initial Data and Vacuum

This paper concerns the barotropic compressible Navier-Stokes equations in a two-dimensional half-space subject to Navier-slip boundary conditions with vacuum or non-vacuum far-field density. The global existence and large-time behavior of weak and strong solutions are established under the assumption that the bulk viscosity coefficient is sufficiently large. It should be remarked that this result is obtained without any restrictions on the size of the initial data. For strong solutions, we derive some a priori decay estimates for the spatial gradient of the velocity field that are uniform with respect to the bulk viscosity coefficient, which play a crucial role in establishing the time-uniform upper bound for the density. Furthermore, we prove that, as the bulk viscosity coefficient tends to infinity, the solutions of the compressible Navier-Stokes equations converge to those of the inhomogeneous incompressible Navier-Stokes equations. In particular, the incompressible limit for weak solutions holds without requiring the initial velocity to be divergence-free.

math.AP↗

arXiv2026

Global Well-Posedness of Classical Solutions to the Multi-Dimensional Degenerate Compressible Navier-Stokes Equations with Large Spherically Symmetric Initial Data

This paper is concerned with the global existence and uniqueness of classical solutions to the barotropic compressible Navier-Stokes equations with degenerate viscosity coefficients in three-dimensional bounded domains or in the whole space $\mathbb{R}^N$ $(N=2,3)$ with non-vacuum far-field density. Specifically, we assume that the shear viscosity coefficient $\mu(\rho)=\rho^\alpha$ and the bulk viscosity coefficient $\lambda(\rho)=(\alpha-1)\rho^\alpha$, which satisfy the BD entropy relation. For arbitrarily large spherically symmetric initial data, we establish the global existence and uniqueness of spherically symmetric classical solutions under the following conditions: for $N=2$, $\alpha \in (0.54369,1)$ and $\gamma \in (1,\infty)$; for $N=3$ (both bounded domains and the whole space), $\alpha \in (0.67661,1)$ and $\gamma \in (1,6\alpha-3)$. In the two-dimensional case $\mathbb{R}^2$, the restriction on $\alpha$ can be further relaxed to $\alpha \in (9-6\sqrt{2},1)$ provided that the initial data satisfy additional weighted integrability conditions. Moreover, we show that the solution will not exhibit vacuum in any finite time provided that no vacuum is present initially.

math.AP↗

arXiv2025

Global Existence and Incompressible Limit for the Three-Dimensional Axisymmetric Compressible Navier-Stokes Equations with Large Bulk Viscosity and Large Initial Data

In this paper, we study the three-dimensional axisymmetric compressible Navier-Stokes equations with slip boundary conditions in a cylindrical domain excluding the axis. We establish the global existence and exponential decay of weak, strong, and classical solutions with large initial data and vacuum, under the assumption that the bulk viscosity coefficient is sufficiently large. Moreover, we prove that as the bulk viscosity coefficient tends to infinity, the solutions of the compressible Navier-Stokes equations converge to those of the inhomogeneous incompressible Navier-Stokes equations.

math.AP↗

arXiv2025

Global Strong Solutions to the Three-Dimensional Axisymmetric Compressible Navier-Stokes Equations with Large Initial Data and Vacuum

This paper investigates the three-dimensional axisymmetric compressible Navier-Stokes equations under slip boundary conditions in a cylindrical domain excluding the axis. For initial density allowed to vanish, we establish the global existence and large time asymptotic behavior of strong and weak solutions, provided the shear viscosity is a positive constant and the bulk one is a power function of density with the power bigger than four-thirds. It should be noted that these results are obtained without any restrictions on the size of initial data. The key idea is to derive a pointwise estimate of the effective viscous flux by exploiting the axisymmetry of the solutions, along with the conformal mapping and the pull back Green's function, and then to cancel out the singularity using the slip boundary conditions.

math.AP↗

arXiv2025

Global Existence and Incompressible Limit for Compressible Navier-Stokes Equations in Bounded Domains with Large Bulk Viscosity and Large Initial Data

We investigate the barotropic compressible Navier-Stokes equations with Navier-slip boundary conditions in a general two-dimensional bounded simply connected domain. For initial data allowing vacuum, we establish the global existence and exponential decay of weak, strong, and classical solutions when the bulk viscosity coefficient is sufficiently large, without any restrictions on the size of the initial data. Furthermore, we prove that, as the bulk viscosity coefficient tends to infinity, solutions of the compressible Navier-Stokes equations converge to those of the inhomogeneous incompressible Navier-Stokes equations. In particular, we establish the incompressible limit of weak solutions without assuming that the initial velocity field is divergence-free.

math.AP↗

arXiv2025

Global Existence and Incompressible Limit of the Cauchy Problem for 2D Compressible Navier-Stokes Equations with Large Bulk Viscosity and Large Initial Data

This paper investigates the Cauchy problem for the barotropic compressible Navier-Stokes equations in $\mathbb{R}^2$ with the constant state as far field, which may be vacuum or non-vacuum. Under the assumption of a sufficiently large bulk viscosity coefficient, we establish the global existence and large time behavior of weak, strong, and classical solutions. It should be mentioned that this result is obtained without any restrictions on the size of the initial data. Moreover, we demonstrate that as the bulk viscosity coefficient tends to infinity, the solutions of the compressible Navier-Stokes equations converge to those of the inhomogeneous incompressible Navier-Stokes equations. The incompressible limit of the weak solutions holds even without requiring the initial velocity to be divergence-free.

math.AP↗

arXiv2025

Global Existence and Incompressible Limit for Compressible Navier-Stokes Equations with Large Bulk Viscosity Coefficient and Large Initial Data

For periodic initial data with the density allowing vacuum, we establish the global existence and exponential decay of weak, strong and classical solutions to the two-dimensional(2D) compressible Navier-Stokes equations when the bulk viscosity coefficient is sufficiently large, without any extra restrictions on initial velocity divergence. Moreover, we demonstrate that when the bulk viscosity coefficient tends to infinity, these solutions converge to solutions to the inhomogeneous incompressible Navier-Stokes equations. For the incompressible limit of weak solutions, our results hold even without requiring the initial velocity field to be divergence-free. Our results are established by introducing time-layers to avoid imposing restrictions on the initial velocity divergence, along with estimates of $L^\infty$ norm of the effective viscous flux $G$ via a time-partitioning approach based on Gagliardo-Nirenberg inequality.

math.AP↗