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Quanrong Li

Publications and source records attributed to Quanrong Li.

5 recordsLinked to original sources
arXiv2022

Stability analysis for the incompressible Navier-Stokes equations with Navier boundary conditions

This paper concerns the instability and stability of the trivial steady states of the incompressible Navier-Stokes equations with Navier-slip boundary conditions in a slab domain in dimension two. The main results show that the stability (or instability) of this constant equilibrium depends crucially on whether the boundaries dissipate energy and the strengthen of the viscosity and slip length. It is shown that in the case that when all the boundaries are dissipative, then nonlinear asymptotic stability holds true, otherwise, there is a sharp critical viscosity, which distinguishes the nonlinear stability from instability.

math.AP↗
arXiv2020

Rayleigh-Taylor instability for nonhomogeneous incompressible fluids with Navier-slip boundary conditions

This paper is concerned with the Rayleigh-Taylor instability for the nonhomogeneous incompressible Navier-Stokes equations with Navier-slip boundary conditions around a steady-state in an infinite slab, where the Navier-slip coefficients do not have defined sign and the slab is horizontally periodic. Motivated by [18], we extend the result from Dirichlet boundary condition to Navier-slip boundary conditions. Our results indicate the factor that "heavier density with increasing height" still plays a key role in the instability under Navier-slip boundary conditions.

math.AP↗
arXiv2019

Global well-posedness of the Navier-Stokes equations with Navier-slip boundary conditions in a strip domain

This paper is concerned with the existence and uniqueness of the strong solution to the incompressible Navier-Stokes equations with Navier-slip boundary conditions in a two-dimensional strip domain where the slip coefficients may not have defined sign. In the meantime, we also establish a number of Gagliardo-Nirenberg inequalities in the corresponding Sobolev spaces which will be applicable to other similar situations.

math.AP↗
arXiv2018

Symmetrical Prandtl boundary layer expansions of steady Navier-Stokes equations on bounded domain

This paper is concerned with the validity of the Prandtl boundary layer theory in the inviscid limit of the steady incompressible Navier-Stokes equations, which is an extension of the pioneer paper (Y. Guo et al., 2017, Ann. PDE) from a domain of $[0,L]\times\mathbb{R}_+$ to $[0,L]\times[0,2]$. Under the symmetry assumption, we establish the validity of the Prandtl boundary layer expansions and the error estimates. The convergence rate as $\e\rightarrow 0$ is also given.

math.AP↗