arXiv subjects

Yeping Li

Publications and source records attributed to Yeping Li.

7 recordsLinked to original sources

arXiv2026

Nonlinear Stability of Taylor-Couette Flows with Heat Buoyancy

This paper investigates the nonlinear stability of Taylor-Couette (TC) flows incorporating the thermal buoyancy within an annular domain characterized by small viscosity $\nu$ and thermal diffusivity $\mu$. It is well established that the buoyancy induced convection significantly impacts practical industrial applications of Taylor-Couette flow \cite{Chen2006}. In contrast to \cite{An.2024}, we specifically examines the influence of the temperature gradients and the gravity on the stability of Taylor-Couette flows in this article. The thermal buoyancy term introduces a destabilizing radial derivative $\partial_r$ into the rotating TC system. To mitigate this destabilizing effect, we employ estimates involving the negative derivatives. Consequently, the additional viscous damping becomes necessary to counterbalance the buoyancy induced instability. Our stability criterion requires that the initial perturbations from the Taylor-Couette flow are bounded by a suitable power of the viscosity. Under this condition, we prove that solutions to the 2D Boussinesq system on $[1, R] \times \mathbb{S}^1$ remain close to the Taylor-Couette flow at the same order.

math.AP↗

arXiv2026

Hydrodynamic limit of the Vlasov-Poisson-Boltzmann system for gas mixture

In this paper, we study the hydrodynamic limit of the Vlasov-Poisson-Boltzmann system for a gas mixture in the whole space $(x \in \mathbb{R}^3)$ with the potential range of $\gamma \in\left(-3, 1\right]$. Using the method of Hilbert expansion, we first derive a bi-Maxwellian determined by the Euler-Poisson system of two fluids. To justify the convergence of the solution rigorously as the Knudsen number tends to zero, we sequentially calculate the first $2k-1$ terms of the expansion series $(k \geq 6)$, and then truncate it, and express the solution as the sum of these first $2k-1$ terms and a remainder term. Within the framework of the $L_{x,v}^2-W_{x,v}^{1,\infty}$ interplay established by Guo and Jang \cite{[ininp]Guo2010CMP}, we construct a new weight function to estimate the remainder term in four different cases regarding the potential $\gamma$. Here, the particle masses $m^A, m^B > 0$ and their charges $e^A, e^B$ can be given arbitrarily. This causes the collision operator to exhibit asymmetric effects ($m^A \neq m^B$), rendering the system of equations impossible to decouple. So, it adds difficulties to both $L^2$, $L^{\infty}$ estimates for the remainder. Therefore, we adopt the framework of vector-valued functions and analyze the velocity decay rate of the operator $K_{M,2,w}^{\alpha,c}$ to eliminate the singularity induced by small parameters in characteristic line iterations. Our results show that the validity time of the solution is $O(\varepsilon^{-y})$, where $y$ is $-\frac{2k-3}{2(2k-1)}$ when $-1 \leq \gamma \leq 1$, and it becomes $-\frac{2k-3}{(1-\gamma)(2k-1)}$, when $-3 < \gamma < -1$. These results possess strong physical realism and can be applied to analyze gas flow dynamics in the daytime ionosphere at high altitudes above the Earth.

math.AP↗

arXiv2023

Asymptotic stability of shock profiles and rarefaction waves to the Navier-Stokes-Poisson system under space-periodic perturbations

This paper concerns with the large-time behaviors of the viscous shock profile and rarefaction wave under initial perturbations which tend to space-periodic functions at infinities for the one-dimensional compressible Navier-Stokes-Poisson equations. It is proved that: (1) for the viscous shock with small strength, if the initial perturbation is suitably small and satisfies a zero-mass type condition, then the solution tends to background viscous shock with a constant shift as time tends to the infinity, and the shift depends on both the mass of the localized perturbation, and the space-periodic perturbation; (2) for the rarefaction wave, if the initial perturbation is suitably small, then the solution tends to background rarefaction wave as time tends to infinity. The proof is based on the delicate constructions of the quadratic ansatzes, which capture the infinitely many interactions between the background waves and the periodic perturbations, and the energy method in Eulerian coordinates involving the effect of self-consistent electric field. Moreover, an abstract lemma is established to distinguish the non-decaying terms and good-decaying terms from the error terms of the equations of the quadratic ansatzes, which will be benefit to constructing the ansatzes and simplifying calculations for other non-localized perturbation problems, especially those with complicatedly coupling physical effects.

math.AP↗

arXiv2017

Asymptotic stability of viscous shock profiles for the 1D compressible Navier-Stokes-Korteweg system with boundary effect

This paper is concerned with the time-asymptotic behavior of strong solutions to an initial-boundary value problem of the compressible Navier-Stokes-Korteweg system on the half line $\mathbb{R}^+$. The asymptotic profile of the problem is shown to be a shifted viscous shock profile, which is suitably away from the boundary. Moreover, we prove that if the initial data around the shifted viscous shock profile and the strength of the shifted viscous shock profile are sufficiently small, then the problem has a unique global strong solution, which tends to the shifted viscous shock profile as time goes to infinity. The analysis is based on the elementary $L^2$-energy method and the key point is to deal with the boundary estimates.

math.AP↗

arXiv2015

Global existence and $L^{p}$ convergence rates of planar waves for three-dimensional bipolar Euler-Poisson systems

In the paper, we consider a multi-dimensional bipolar hydrodynamic model from semiconductor devices and plasmas. This system takes the form of Euler-Poisson with electric field and frictional damping added to the momentum equations. We show the global existence and $L^{p}$ convergence rates of planar diffusion waves for multi-dimensional bipolar Euler-Poisson systems when the initial data are near the planar diffusive waves. A frequency decomposition and approximate Green function based on delicate energy method are used to get the optimal decay rates of the planar diffusion waves. To our knowledge, the $L^p(p\in[2,+\infty])$-convergence rate of planar waves improves the previous results about the $L^2$-convergence rates.

math-ph↗

arXiv2010

Eight new quasars discovered by LAMOST in one extragalactic field

We report the discovery of eight new quasars in one extragalactic field (five degree centered at RA=$08^h58^m08.2^s$, Dec=$01^o32'29.7''$) with the LAMOST commissioning observations on December 18, 2009. These quasars, with $i$ magnitudes from 16.44 to 19.34 and redshifts from 0.898 to 2.773, were not identified in the SDSS spectroscopic survey, though six of them with redshifts less than 2.5 were selected as quasar targets in SDSS. Except one source without near-IR $Y$-band data, seven of these eight new quasars meet a newly proposed quasar selection criterion involving both near-IR and optical colors. Two of them were found in the 'redshift desert' for quasars ($z$ from 2.2 to 3), indicating that the new criterion is efficient for recovering the missing quasars with similar optical colors as stars. Although LAMOST met some problems during the commissioning observations, we were still able to identify other 38 known SDSS quasars in this field, with $i$ magnitudes from 16.24 to 19.10 and redshifts from 0.297 to 4.512. Our identifications imply that a substantial fraction of quasars may be missing in the previous quasar surveys. The implication of our results to the future LAMOST quasar survey is discussed.

astro-ph.CO↗

arXiv2010

A very bright i=16.44 quasar in the `redshift desert' discovered by LAMOST

The redshift range from 2.2 to 3, is known as the 'redshift desert' of quasars because quasars with redshift in this range have similar optical colors as normal stars and are thus difficult to be found in optical sky surveys. A quasar candidate, SDSS J085543.40-001517.7, which was selected by a recently proposed criterion involving near-IR $Y-K$ and optical $g-z$ colors, was identified spectroscopically as a new quasar with redshift of 2.427 by the LAMOST commissioning observation in December 2009 and confirmed by the observation made with the NAOC/Xinglong 2.16m telescope in March 2010. This quasar was not targeted in the SDSS spectroscopic survey because it locates in the stellar locus of the optical color-color diagrams, while it is clearly separated from stars in the $Y-K$ vs. $g-z$ diagram. Comparing with other SDSS quasars we found this new quasar with $i$ magnitude of 16.44 is apparently the brightest one in the redshift range from 2.3 to 2.7. From the spectral properties we derived its central black hole mass as $(1.4\sim3.9) \times 10^{10} M_\odot$ and the bolometric luminosity as $3.7\times 10^{48}$ \ergs, which indicates that this new quasar is intrinsically very bright and belongs to the most luminous quasars in the universe. Our identification supports that quasars in the redshift desert can be found by the quasar selection criterion involving the near-IR colors. More missing quasars are expected to be recovered by the future LAMOST spectroscopic surveys, which is important to the study of the cosmological evolution of quasars at redshift higher than 2.2.

astro-ph.CO↗