Ling-Yun Shou

Ling-Yun Shou
Nanjing Normal University · School of Mathematical & Computer Science

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29
Publications
1,557
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49
Citations
Introduction
Nonlinear Partial differential equations, Fourier analysis

Publications

Publications (29)
Preprint
This paper concerns the global-in-time evolution of a generic compressible two-fluid model in $\mathbb{R}^d$ ($d\geq3$) with the common pressure law. Due to the non-dissipative properties for densities and two different particle paths caused by velocities, the system lacks the usual symmetry structure and is partially dissipative in the sense that...
Preprint
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We investigate the incompressible inhomogeneous magnetohydrodynamic equations in $\mathbb{R}^3$, under the assumptions that the initial density $\rho_0$ is only bounded, and the initial velocity $u_0$ and magnetic field $B_0$ exhibit critical regularities. In particular, the density is allowed to be piecewise constant with jumps. First, we establis...
Article
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The low-frequency $L^1$ assumption has been extensively applied to the large-time asymptotics of solutions to the compressible Navier-Stokes equations and incompressible Navier-Stokes equations since the classical efforts due to Kawashima, Matsumura, Nishida, Ponce, Schonbek and Wiegner. In this paper, we establish a sharp decay characterization fo...
Preprint
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We construct a unique global solution to the Cauchy problem of the 3D Boltzmann equation for initial data around the Maxwellian in the {\emph{homogeneous}} spatially critical Besov space \widetilde{L}^2_{\xi}(\dot{B}_{2,1}^{1/2}\cap\dot{B}_{2,1}^{3/2}). In addition, under the condition that the low-frequency part of initial perturbation is bounded...
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We consider the chemotaxis-Navier-Stokes system with generalized fluid dissipation in $\mathbb{R}^3$: \begin{eqnarray*} \begin{cases} \partial_t n+u\cdot \nabla n=\Delta n- \nabla \cdot (\chi(c)n \nabla c),\\ \partial_t c+u \cdot \nabla c=\Delta c-nf(c),\\ \partial_t u +u \cdot \nabla u+\nabla P=-(-\Delta)^\alpha u-n\nabla \phi,\\ \nabla \cdot u=0,...
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We are concerned with a system governing the evolution of the pressureless compressible Euler equations with Riesz interaction and damping in $\mathbb{R}^{d}$ ($d\geq1$), where the interaction force is given by $\nabla(-\Delta)^{\smash{\frac{\alpha-d}{2}}}(\rho-\bar{\rho})$ with $d-2<\alpha<d$. Referring to the standard dissipative structure of fir...
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We investigate the three-dimensional compressible Euler-Maxwell system, a model for simulating the transport of electrons interacting with propagating electromagnetic waves in semiconductor devices. First, we show the global well-posedness of classical solutions being a sharp small perturbation of constant equilibrium in a critical regularity setti...
Article
A new framework to obtain time-decay estimates for partially dissipative hyperbolic systems set on the real line is developed. Under the classical Shizuta–Kawashima (SK) stability condition, equivalent to the Kalman rank condition in control theory, the solutions of these systems decay exponentially in time for high frequencies and polynomially for...
Article
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In this paper, we study the asymptotic behaviors of solutions to the inhomogeneous Navier-Stokes-Vlasov system in R3 × R3, where the initial fluid density is allowed to vanish. We establish the uniform bound of the macroscopic density associated with the distribution function and prove the global existence and uniqueness of strong solutions to the...
Article
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We derive a novel two-phase flow system in porous media as a relaxation limit of compressible multi-fluid systems. Considering a one-velocity Baer–Nunziato system with friction forces, we first justify its pressure-relaxation limit toward a Kapila model in a uniform manner with respect to the time-relaxation parameter associated with the friction f...
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In this paper, we study the asymptotic behaviors of solutions to the inhomogeneous Navier- Stokes-Vlasov system in R3 × R3, where the initial fluid density is allowed to vanish. We establish the uniform bound of the macroscopic density associated with the distribution function and prove the global existence and uniqueness of strong solutions to the...
Preprint
Full-text available
The low-frequency $L^1$ assumption has been extensively applied to the large-time asymptotics of solutions to the compressible Navier-Stokes equations and incompressible Navier-Stokes equations since the classical efforts due to Matsumura & Nishida, Ponce, Schonbek and Wiegner. In this paper, we establish a sharp decay characterization for the comp...
Preprint
Full-text available
A new framework to obtain time-decay estimates for partially dissipative hyperbolic systems set on the real line is developed. Under the classical Shizuta-Kawashima (SK) stability condition, equivalent to the Kalman rank condition in control theory, the solutions of these systems decay exponentially in time for high frequencies and polynomially for...
Article
We study the diffusive relaxation limit of the Jin-Xin system toward viscous conservation laws in the multi-dimensional setting. For initial data being small perturbations of a constant state in suitable homogeneous Besov norms, we prove the global well-posedness of strong solutions satisfying uniform estimates with respect to the relaxation parame...
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In this paper, we consider the Cauchy problem of the multi-dimensional compressible Navier-Stokes-Euler system for two-phase flow motion, which consists of the isentropic compressible Navier-Stokes equations and the isothermal compressible Euler equations coupled with each other through a relaxation drag force. We first establish the local existenc...
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The one-dimensional compressible Navier-Stokes-Vlasov-Fokker- Planck system with density-dependent viscosity and drag force coefficients is investigated in the present paper. The existence, uniqueness, and regularity of global weak solution to the initial value problem for general initial data are established in spatial periodic domain. Moreover, t...
Preprint
Full-text available
We study the diffusive relaxation limit of the Jin-Xin system toward viscous conservation laws in the multi-dimensional setting. For initial data being small perturbations of a constant state in suitable homogeneous Besov norms, we prove the global well-posedness of strong solutions satisfying uniform estimates with respect to the relaxation parame...
Preprint
Full-text available
In this paper we investigate two types of relaxation processes quantitatively in the context of small data global-in-time solutions for compressible one-velocity multi-fluid models. First, we justify the pressure-relaxation limit from a one-velocity Baer-Nunziato system to a Kapila model as the pressure-relaxation parameter tends to zero, in a unif...
Article
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The initial value problem of the multi-dimensional drift-flux model for two-phase flow is investigated in this paper, and the global existence of weak solutions with finite energy is established for general pressure- density functions without the monotonicity assumption.
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In this paper, we consider a two-phase flow model consisting of the compressible Navier-Stokes equations with degenerate viscosity coupled with the compressible Navier-Stokes equations with constant viscosities via a drag force, which can be derived from Chapman-Enskog expansion for the compressible Navier-Stokes-Vlasov-Fokker-Planck system. For ge...
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An Euler-type hyperbolic-parabolic system of chemotactic aggregation describing the vascular network formation is investigated in the critical regularity setting. For initial data near a constant equilibrium state, the global well-posedness of the classical solution to the Cauchy problem with general pressure laws is proved in critical hybrid Besov...
Preprint
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The initial value problem to the multi-dimensional drift-flux model for two-phase flow is investigated in this paper, and the global existence of weak solutions with finite energy is established for general pressure-density functions without the monotonicity assumption.
Article
A fluid-particle model is investigated in the present paper, which consists of the compressible Navier-Stokes equations coupled with the Vlasov equation though a nonlinear drag force. We consider the initial value problem for the one-dimensional compressible Navier-Stokes-Vlasov system and establish the global existence and uniqueness of the weak s...
Preprint
Full-text available
The one-dimensional compressible Navier-Stokes-Vlasov-Fokker-Planck system with density-dependent viscosity and drag force coefficients is investigated in the present paper. The existence, uniqueness, and regularity of global weak solution to the initial value problem for general initial data are established in spatial periodic domain. Moreover, th...
Preprint
Full-text available
A fluid-particle model is investigated in the present paper, which consists of the compressible Navier-Stokes equations coupled with the Vlasov equation though a nonlinear drag force. We consider the initial value problem for the one-dimensional compressible Navier-Stokes-Vlasov system and establish the global existence and uniqueness of the weak s...

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