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Chunhui Zhou

Publications and source records attributed to Chunhui Zhou.

16 recordsLinked to original sources
arXiv2025

Structure stability of steady supersonic shear flow with inflow boundary conditions

We study the existence and zero viscous limit of smooth solutions to steady compressible Navier-Stokes equations near plane shear flow between two moving parallel walls. Under the assumption $0<L\ll1$, we prove that for any plane supersonic shear flow $\mathbf{U}^0=(μ(x_2),0)$, there exist smooth solutions near $\mathbf{U}^0$ to steady compressible Navier-Stokes equations in a 2-dimension domain $Ω=(0,L)\times (0,2)$. Moreover, based on the uniform-in-$\varepsilon$ estimates, we establish the zero viscosity limit of the solutions obtained above to the solutions of the steady Euler equations.

math.AP↗
arXiv2025

Unmanned Surface Vehicle Path Planning from the Perspective of Multi-Modality Constraints: A Comprehensive Analysis

The essence of the path planning problems is multi-modality constraint. However, most of the current literature has not mentioned this issue. This paper introduces the research progress of path planning based on the multi-modality constraint. The path planning of multi-modality constraint research can be classified into three stages in terms of its basic ingredients (such as shape, kinematics and dynamics et al.): Route Planning, Trajectory Planning and Motion Planning. It then reviews the research methods and classical algorithms, especially those applied to the Unmanned Surface Vehicle (USV) in every stage. Finally, the paper points out some existing problems in every stage and suggestions for future research.

cs.RO↗
arXiv2024

The loop equation for the Burgers--KdV hierarchy

The Burgers--KdV hierarchy was introduced towards understanding intersection numbers on the moduli space of Riemann surfaces with boundaries. The goal of this paper is to derive the Dubrovin--Zhang type loop equation for the topological tau-function of the Burgers--KdV hierarchy. As as application, we provide some relations for open intersection numbers.

math-ph↗
arXiv2024

Zero Viscosity Limit of Steady Compressible Shear Flow with Navier-Slip Boundary

We investigate the existence and the zero viscosity limit of steady compressible shear flow with Navier-slip boundary condition in the absence of any external force in a two-dimension domain $Ω=(0,L)\times(0,2)$. More precisely, under the assumption that the Mach number $η<\va^{\f12+}$ and $L\ll1$, we prove the existence of smooth solutions to steady compressible Naiver-Stokes equations near plane Poiseuille-Couette flow as well as the convergence of the solutions obtained above to the solutions of steady incompressible Euler equations when the viscous $\va$ tends to zero.

math.AP↗
arXiv2024

Analysis of the Impact of Central bank Digital Currency on the Demand for Transactional Currency

This paper takes the development of Central bank digital currencies as a perspective, introduces it into the Baumol-Tobin money demand theoretical framework, establishes the transactional money demand model under Central bank Digital Currency, and qualitatively analyzes the influence mechanism of Central bank digital currencies on transactional money demand; meanwhile, quarterly data from 2010-2022 are selected to test the relationship between Central bank digital currencies and transactional money demand through the ARDL model. The long-run equilibrium and short-run dynamics between the demand for Central bank digital currencies and transactional currency are examined by ARDL model. The empirical results show that the issuance and circulation of Central bank digital currencies will reduce the demand for transactional money. Based on the theoretical analysis and empirical test, this paper proposes that China should explore a more effective Currency policy in the context of Central bank digital currencies while promoting the development of Central bank digital currencies in a prudent manner in the future.

econ.GN↗
arXiv2023

Empirical Analysis of the Impact of Legal Tender Digital Currency on Monetary Policy -Based on China's Data

This paper takes the development of China's Central bank digital currencies as a perspective, theoretically analyses the impact mechanism of the issuance and circulation of Central bank digital currencies on China's monetary policy and various variables of the money multiplier; at the same time, it selects the quarterly data from 2010 to 2022, and examines the impact of the Central bank digital currencies on the money supply multiplier through the establishment of the VECM model. The research results show that: the issuance of China's Central bank digital currencies will have an impact on the effectiveness of monetary policy and intermediary indicators; and have a certain positive impact on the narrow money multiplier and broad money multiplier. Based on theoretical analyses and empirical tests, this paper proposes that China should explore a more effective monetary policy in the context of Central bank digital currencies in the future on the premise of steadily promoting the development of Central bank digital currencies.

econ.GN↗
arXiv2022

Stability and related zero viscosity limit of steady plane Poiseuille-Couette flows with no-slip boundary condtion

We prove the existence and stability of smooth solutions to the steady Navier-Stokes equations near plane Poiseuille-Couette flow. Consequently, we also provide the zero viscosity limit of the 2D steady Navier-Stokes equations to the steady Euler equations. First, in the absence of any external force, we prove that there exist smooth solutions to the steady Navier-Stokes equations which are stable under infinitesimal perturbations of plane Poiseuille-Couette flow. In particular, if the basic flow is the Couette flow, then we can prove that the flow is stable for any finite perturbation small enough. Moreover, we also show that, if we put a proper external force to control the flow, then we can also obtain a large class of smooth solution of the steady Navier-Stokes equations which is stable for infinitesimal perturbation of the external force. Finally, based on the same linear estimates, we establish the zero viscosity limit of all the solutions obtained above to the solutions of the Euler equations.

math.AP↗
arXiv2021

Gelfand--Dickey hierarchy, generalized BGW tau-function, and $W$-constraints

Let $r\geq 2$ be an integer. The generalized BGW tau-function for the Gelfand--Dickey hierarchy of $(r-1)$ dependent variables (aka the $r$-reduced KP hierarchy) is defined as a particular tau-function that depends on $(r-1)$ constant parameters $d_1,\dots,d_{r-1}$. In this paper we show that this tau-function satisfies a family of linear equations, called the $W$-constraints of the second kind. The operators giving rise to the linear equations also depend on $(r-1)$ constant parameters. We show that there is a one-to-one correspondence between the two sets of parameters.

math-ph↗
arXiv2021

On an extension of the generalized BGW tau-function

For an arbitrary solution to the Burgers--KdV hierarchy, we define the tau-tuple $(τ_1,τ_2)$ of the solution. We show that the product $τ_1τ_2$ admits Buryak's residue formula. Therefore, according to Alexandrov's theorem, $τ_1τ_2$ is a tau-function of the KP hierarchy. We then derive a formula for the affine coordinates for the point of the Sato Grassmannian corresponding to the tau-function $τ_1τ_2$ explicitly in terms of those for $τ_1$. Applications to the analogous open extension of the generalized BGW tau-function and to the open partition function are given.

math-ph↗
arXiv2020

The Loop Equation for Special Cubic Hodge Integrals

As the first step of proving the Hodge-FVH correspondence recently proposed in [19], we derive the Virasoro constraints and the Dubrovin--Zhang loop equation for special cubic Hodge integrals. We show that this loop equation has a unique solution, and provide a new algorithm for the computation of these Hodge integrals. We also observe the gap phenomenon for certain special cubic Hodge free energies.

math.AG↗
arXiv2020

The Hodge-FVH Correspondence

The Hodge-FVH correspondence establishes a relationship between the special cubic Hodge integrals and an integrable hierarchy, which is called the fractional Volterra hierarchy. In this paper we prove this correspondence. As an application of this result, we prove a gap condition for certain special cubic Hodge integrals and give an algorithm for computing the coefficients that appear in the gap condition.

math-ph↗
arXiv2017

Stationary Inviscid Limit to Shear Flows

In this note we establish a density result for certain stationary shear flows, $μ(y)$, that vanish at the boundaries of a horizontal channel. We construct stationary solutions to 2D Navier-Stokes that are $ε$-close in $L^\infty$ to the given shear flow. Our construction is based on a coercivity estimate for the Rayleigh operator, $R[v]$, which is based on a decomposition made possible by the vanishing of $μ$ at the boundaries.

math.AP↗
arXiv2017

Fractional Volterra Hierarchy

The generating function of cubic Hodge integrals satisfying the local Calabi-Yau condition is conjectured to be a tau function of a new integrable system which can be regarded as a fractional generalization of the Volterra lattice hierarchy, so we name it the fractional Volterra hierarchy. In this paper, we give the definition of this integrable hierarchy in terms of Lax pair and Hamiltonian formalisms, construct its tau functions, and present its multi-soliton solutions.

nlin.SI↗
arXiv2013

On the existence of weak solutions to the three-dimensional steady compressible Navier-Stokes equations in bounded domains

We prove the existence of a weak solution to the three-dimensional steady compressible isentropic Navier-Stokes equations in bounded domains for any specific heat ratio γ> 1. Generally speaking, the proof is based on the new weighted estimates of both pressure and kinetic energy for the approximate system which result in some higher integrability of the density, and the method of weak convergence. Comparing with [12] where the spatially periodic case was studied, here we have to control the additional integral terms of both pressure and kinetic energy involving with the points near the boundary which become degenerate when the points approach the boundary. Such integral terms are estimated using some new techniques, i.e., we use the techniques of the mirror image and boundary straightening to prove that the weighted estimates of both pressure and kinetic energy for the points near the boundary can be controlled by the weighted estimates for the points on the boundary. Moreover, we prove that once the weighted estimates of the kinetic energy in the direction of the unit normal to the boundary are bounded, we can control the weighted estimates of the total energy on the boundary.

math.AP↗
arXiv2013

Proof of a Conjecture on the Genus Two Free Energy Associated to the A_n Singularity

In a recent paper [8], it is proved that the genus two free energy of an arbitrary semisimple Frobenius manifold can be represented as a sum of contributions associated with dual graphs of certain stable algebraic curves of genus two plus the so called genus two G-function, and for a certain class of Frobenius manifolds it is conjectured that the associated genus two G-function vanishes. In this paper, we prove this conjecture for the Frobenius manifolds associated with simple singularities of type A.

math-ph↗