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Yan Guo

Publications and source records attributed to Yan Guo.

At least 73 records · Page 4Linked to original sources
arXiv2018

Validity of Steady Prandtl Layer Expansions

Let the viscosity $\varepsilon \rightarrow 0$ for the 2D steady Navier-Stokes equations in the region $0\leq x\leq L$ and $0\leq y<\infty$ with no slip boundary conditions at $y=0$. For $L<<1$, we justify the validity of the steady Prandtl layer expansion for scaled Prandtl layers, including the celebrated Blasius boundary layer. Our uniform estimates in $\varepsilon$ are achieved through a fixed-point scheme: \begin{equation*} [u^{0}, v^0] \overset{\text{DNS}^{-1}}{\longrightarrow }v\overset{\mathcal{L}^{-1}}{ \longrightarrow }[u^{0}, v^0] \label{fixedpoint} \end{equation*} for solving the Navier-Stokes equations, where $[u^{0}, v^0]$ are the tangential and normal velocities at $x=0,$ DNS stands for $\partial _{x}$ of the vorticity equation for the normal velocity $v$, and $\mathcal{L}$ the compatibility ODE for $[u^{0}, v^0]$ at $x=0.$

math.AP↗
arXiv2018

Steady Prandtl Layer Expansions with External Forcing

In this article we apply the machinery developed in Guo-Iyer[1] together with a new compactness estimate and an object called the degree in order to prove validity of steady Prandtl layer expansions with external forcing.

math.AP↗
arXiv2017

Study of $Υ(nS)$ ${\to}$ $B_{c}P$ decays with perturbative QCD approach

With the potential prospects of the $Υ(nS)$ at high-luminosity dedicated heavy-flavor factories, the color-favored $Υ(nS)$ ${\to}$ $B_{c}π$, $B_{c}K$ weak decays are studied with the pQCD approach. It is found that branching ratios for the $Υ(nS)$ ${\to}$ $B_{c}π$ decay are as large as the order of ${\cal O}(10^{-11})$, which might be measured promisingly by the future experiments.

hep-ph↗
arXiv2017

The existence of stable BGK waves

The 1D Vlasov-Poisson system is the simplest kinetic model for describing an electrostatic collisonless plasma, and the BGK waves are its famous exact steady solutions. They play an important role on the long time dynamics of a collisionless plasma as potential "final states" or "attractors", thanks to many numerical simulations and observations. Despite their importance, the existence of stable BGK waves has been an open problem since their discovery in 1958. In this paper, first linearly stable BGK waves are constructed near homogeneous states.

math.AP↗
arXiv2016

Incompressible hydrodynamic approximation with viscous heating to the Boltzmann equation

The incompressible Navier-Stokes-Fourier system with viscous heating was first derived from the Boltzmann equation in the form of the diffusive scaling by Bardos-Levermore-Ukai-Yang (2008). The purpose of this paper is to justify such an incompressible hydrodynamic approximation to the Boltzmann equation in $L^2\cap L^\infty$ setting in a periodic box. Based on an odd-even expansion of the solution with respect to the microscopic velocity, the diffusive coefficients are determined by the incompressible Navier-Stokes-Fourier system with viscous heating and the super Burnett functions. More importantly, the remainder of the expansion is proven to decay exponentially in time via an $L^2-L^\infty$ approach on the condition that the initial data satisfies the mass, momentum and energy conversation laws.

math.AP↗
arXiv2016

A $L^{2}$ to $L^{\infty}$ approach for the Landau Equation

Consider the Landau equation with Coulomb potential in a periodic box. We develop a new $L^{2}\rightarrow L^{\infty }$ framework to construct global unique solutions near Maxwellian with small $L^{\infty }\ $norm. The first step is to establish global $L^{2}$ estimates with strong velocity weight and time decay, under the assumption of $L^{\infty }$ bound, which is further controlled by such $L^{2}$ estimates via De Giorgi's method \cite{golse2016harnack} and \cite{mouhot2015holder}. The second step is to employ estimates in $S_{p}$ spaces to control velocity derivatives to ensure uniqueness, which is based on Holder estimates via De Giorgi's method \cite{golse2016harnack}, \cite{golse2015holder}, and \cite{mouhot2015holder}.

math.AP↗
arXiv2016

Regularity of Milne Problem with Geometric Correction in 3D

Consider the Milne problem with geometric correction in a 3D convex domain. Via bootstrapping arguments, we establish $W^{1,\infty}$ regularity for its solutions. Combined with a uniform $L^6$ estimate, such regularity leads to the validity of diffusive expansion for the neutron transport equation with diffusive boundary conditions.

math.AP↗
arXiv2016

Asymptotic Stability of the Boltzmann Equation with Maxwell Boundary Conditions

In a general $C^1$ domain, we study the perturbative Cauchy theory for the Boltzmann equation with Maxwell boundary conditions with an accommodation coefficient $α$ in $(\sqrt{2/3},1]$, and discuss this threshold. We consider polynomial or stretched exponential weights $m(v)$ and prove existence, uniqueness and exponential trend to equilibrium around a global Maxwellian in $L^\infty_{x,v}(m)$. Of important note is the fact that the methods do not involve contradiction arguments.

math.AP↗
arXiv2016

Pulse Shaped OFDM for 5G Systems

OFDM-based waveforms with filtering or windowing functionalities are considered key enablers for a flexible air-interface design for multi-service support in future 5G systems. One candidate from this category of waveforms is pulse shaped OFDM, which follows the idea of subcarrier filtering and aims at fully maintaining the advantages of standard OFDM systems while addressing their drawbacks. In this paper, we elaborate on several pulse shaping design methods, and show how pulse shapes can be exploited as an additional degree of freedom to provide better frequency localization and more efficient spectrum utilization under a pre-defined spectrum mask. The performance analysis and evaluation results show that, for a practical mobile communication systems, the application of pulse shaping is a simple and effective means to achieve a lower out-of-band leakage for OFDM systems at virtually no costs. In fact, the complexity increase amounts to 1-2% compared to CP-OFDM only. In addition, the system's robustness against both time and frequency distortions is shown to be substantially improved by a proper pulse shape design. By allowing for the flexible configuration of physical layer parameters per sub-band according to the diverse requirements of future 5G services, pulse shaped OFDM systems can efficiently facilitate asynchronous transmissions and fragmented spectrum access, rendering it beneficial for various mobile-broadband and Internet-of-Things applications.

cs.IT↗
arXiv2016

Geometric Correction in Diffusive Limit of Neutron Transport Equation in 2D Convex Domains

Consider the steady neutron transport equation with diffusive boundary condition. In [Wu and Guo(2015) Comm. Math. Phys.] and [Wu and Yang and Guo(2016) Preprint], it was discovered that geometric correction is necessary for the Milne problem of Knudsen-layer construction in a disk or annulus. In this paper, we establish diffusive limit for a 2D convex domain. Our contribution relies on novel $W^{1,\infty}$ estimates for the Milne problem with geometric correction in the presence of a convex domain, as well as an $L^{2m}-L^{\infty}$ framework which yields stronger remainder estimates.

math.AP↗
arXiv2016

Asymptotic Analysis of Transport Equation in Annulus

We consider the diffusive limit of a steady neutron transport equation with one-speed velocity in a two-dimensional annulus. A classical theorem states that the solution can be approximated in $L^{\infty}$ by the leading order interior solution plus the corresponding Knudsen layers in the diffusive limit. In this paper, we construct a counterexample of this result via a different boundary layer expansion with geometric correction.

math.AP↗
arXiv2016

The Boltzmann equation with weakly inhomogeneous data in bounded domain

This paper is concerned with the Boltzmann equation with specular reflection boundary condition. We construct a unique global solution and obtain its large time asymptotic behavior in the case that the initial data is close enough to a radially symmetric homogeneous datum. The result extends the case of Cauchy problem considered by Arkeryd-Esposito-Pulvirenti [Comm. Math. Phys. 111(3): 393-407 (1987)] to the specular reflection boundary value problem in bounded domain.

math.AP↗
arXiv2016

Existence and BV-regularity for Neutron transport equation in non-convex domain

This paper considers the neutron transport equation in bounded domain with a combination of the diffusive boundary condition and the in-flow boundary condition. We firstly study the existence of solution in any fixed time by $L^2-L^{\infty}$ method, which was established to study Boltzmann equation in \cite{[Guo2]}. Based on the uniform estimates of the solution, we also consider the BV-regularity of the solution in non-convex domain. A cut-off function, which aims to exclude all the characteristics emanating from the grazing set $\mathfrak{S}_B$, has been constructed precisely.

math.AP↗
arXiv2016

Stationary solutions to the Boltzmann equation in the Hydrodynamic limit

Despite its conceptual and practical importance, the rigorous derivation of the steady incompressible Navier-Stokes-Fourier system from the Boltzmann theory has been {an} outstanding {open problem} for general domains in 3D. We settle this open question in {the} affirmative, in the presence of a small external field and a small boundary temperature variation for the diffuse boundary condition. We employ a recent quantitative $L^{2}-L^{\infty }$ approach with new $L^{6}$ estimates for the hydrodynamic part $\mathbf{P}f$ of the distribution function. Our results also imply the validity of Fourier law in the hydrodynamical limit, and our method {leads to {asymptotical} stability of steady Boltzmann solutions as well as the derivation of the {unsteady} Navier-Stokes Fourier system}.

math.AP↗
arXiv2016

Stability of contact lines in fluids: 2D Stokes Flow

In an effort to study the stability of contact lines in fluids, we consider the dynamics of an incompressible viscous Stokes fluid evolving in a two-dimensional open-top vessel under the influence of gravity. This is a free boundary problem: the interface between the fluid in the vessel and the air above (modeled by a trivial fluid) is free to move and experiences capillary forces. The three-phase interface where the fluid, air, and solid vessel wall meet is known as a contact point, and the angle formed between the free interface and the vessel is called the contact angle. We consider a model of this problem that allows for fully dynamic contact points and angles. We develop a scheme of a priori estimates for the model, which then allow us to show that for initial data sufficiently close to equilibrium, the model admits global solutions that decay to equilibrium exponentially fast.

math.AP↗
arXiv2014

On the Weak Coupling Limit of Quantum Many-body Dynamics and the Quantum Boltzmann Equation

The rigorous derivation of the Uehling-Uhlenbeck equation from more fundamental quantum many-particle systems is a challenging open problem in mathematics. In this paper, we exam the weak coupling limit of quantum N-particle dynamics. We assume the integral of the microscopic interaction is zero and we assume W^{4,1} per-particle regularity on the coressponding BBGKY sequence so that we can rigorously commute limits and integrals. We prove that, if the BBGKY sequence does converge in some weak sense, then this weak-coupling limit must satisfy the infinite quantum Maxwell-Boltzmann hierarchy instead of the expected infinite Uehling-Uhlenbeck hierarchy, regardless of the statistics the particles obey. Our result indicates that, in order to derive the Uehling-Uhlenbeck equation, one must work with per-particle regularity bound below W^{4,1}.

math.AP↗
arXiv2014

Prandtl boundary layer expansions of steady Navier-Stokes flows over a moving plate

This paper concerns the validity of the Prandtl boundary layer theory in the inviscid limit for steady incompressible Navier-Stokes flows. The stationary flows, with small viscosity, are considered on $[0,L]\times \mathbb{R}_{+}$, assuming a no-slip boundary condition over a moving plate at $y=0$. We establish the validity of the Prandtl boundary layer expansion and its error estimates.

math.AP↗