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学者姓名：黎勇
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Abstract ：
In this paper, an initial boundary value problem of the 2D incompressible Benard system is concerned. The global existence of a unique strong solution is established by the energy method and a key logarithmic interpolation inequality. In particular, the exponential decay rates for the gradients of velocity and temperature field are obtained.
Keyword ：
exponential decay exponential decay nonhomogeneous Benard system nonhomogeneous Benard system global existence global existence vacuum vacuum density dependent density dependent
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| GB/T 7714 | Liu, Min , Li, Yong . Global existence and exponential decay of the 2D density-dependent Bénard system with vacuum in bounded domain [J]. | MATHEMATICAL METHODS IN THE APPLIED SCIENCES , 2024 , 47 (11) : 8840-8856 . |
| MLA | Liu, Min 等. "Global existence and exponential decay of the 2D density-dependent Bénard system with vacuum in bounded domain" . | MATHEMATICAL METHODS IN THE APPLIED SCIENCES 47 . 11 (2024) : 8840-8856 . |
| APA | Liu, Min , Li, Yong . Global existence and exponential decay of the 2D density-dependent Bénard system with vacuum in bounded domain . | MATHEMATICAL METHODS IN THE APPLIED SCIENCES , 2024 , 47 (11) , 8840-8856 . |
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Abstract ：
In this paper, we study the Cauchy problem of the incompressible Be ' nard system with density-dependent viscosity on the whole three-dimensional space. We first construct a key priori exponential estimates by the energy method, and then we prove that there is a unique global strong solution for the 3D Cauchy problem under the assumption that initial energy is suitably small. In particular, it is not required to be smallness condition for the initial density which contains vacuum and even has compact support. Finally, we obtain the exponential decay rates for the gradients of velocity, temperature field and pressure.
Keyword ：
Benard system Benard system density-dependent density-dependent exponen-tial decay rates exponen-tial decay rates global well-posedness global well-posedness vacuum vacuum
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| GB/T 7714 | Liu, Min , Li, Yong . Global strong solution and exponential decay to the 3D incompressible Benard system with density-dependent viscosity and vacuum [J]. | DYNAMICS OF PARTIAL DIFFERENTIAL EQUATIONS , 2023 , 20 (2) : 117-133 . |
| MLA | Liu, Min 等. "Global strong solution and exponential decay to the 3D incompressible Benard system with density-dependent viscosity and vacuum" . | DYNAMICS OF PARTIAL DIFFERENTIAL EQUATIONS 20 . 2 (2023) : 117-133 . |
| APA | Liu, Min , Li, Yong . Global strong solution and exponential decay to the 3D incompressible Benard system with density-dependent viscosity and vacuum . | DYNAMICS OF PARTIAL DIFFERENTIAL EQUATIONS , 2023 , 20 (2) , 117-133 . |
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Abstract ：
In this paper, we are devoted to study the Cauchy problem of the incompressible density-dependent Boussinesq equations of Korteweg type with vacuum. We establish some key spatial weighted estimates and a priori decay-in-time rate of the strong solutions by using the energy method. Furthermore, we prove that there is a unique global strong solution for the 2D Cauchy problem when the spatial weighted norm of the initial density is suitably small. Finally, we also obtain the large time decay rates for the gradients of velocity, temperature and pressure.(c) 2022 Elsevier Ltd. All rights reserved.
Keyword ：
Korteweg type Korteweg type Vacuum Vacuum Boussinesq equations Boussinesq equations Long time behavior Long time behavior Well-posedness Well-posedness
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| GB/T 7714 | Liu, Min , Li, Yong . Global well-posedeness and large time asymptotic behavior of 2D density-dependent Boussinesq equations of Korteweg type with vacuum [J]. | NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS , 2023 , 70 . |
| MLA | Liu, Min 等. "Global well-posedeness and large time asymptotic behavior of 2D density-dependent Boussinesq equations of Korteweg type with vacuum" . | NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS 70 (2023) . |
| APA | Liu, Min , Li, Yong . Global well-posedeness and large time asymptotic behavior of 2D density-dependent Boussinesq equations of Korteweg type with vacuum . | NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS , 2023 , 70 . |
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Abstract ：
In this paper, we investigate the nonlinear stability of contact waves for the Cauchy problem to the compressible Navier-Stokes equations for a reacting mixture in one dimension. If the corresponding Riemann problem for the compressible Euler system admits a contact discontinuity solution, it is shown that the contact wave is nonlinearly stable, while the strength of the contact discontinuity and the initial perturbation are suitably small. Especially, we obtain the convergence rate by using anti-derivative methods and elaborated energy estimates.
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| GB/T 7714 | Peng, Lishuang , Li, Yong . Decay rate to contact discontinuities for the one-dimensional compressible Navier-Stokes equations with a reacting mixture [J]. | JOURNAL OF MATHEMATICAL PHYSICS , 2023 , 64 (6) . |
| MLA | Peng, Lishuang 等. "Decay rate to contact discontinuities for the one-dimensional compressible Navier-Stokes equations with a reacting mixture" . | JOURNAL OF MATHEMATICAL PHYSICS 64 . 6 (2023) . |
| APA | Peng, Lishuang , Li, Yong . Decay rate to contact discontinuities for the one-dimensional compressible Navier-Stokes equations with a reacting mixture . | JOURNAL OF MATHEMATICAL PHYSICS , 2023 , 64 (6) . |
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Abstract ：
In this paper, we study the combined quasi-neutral and zero-viscosity limits of the two-fluid Navier-Stokes-Poisson system for a plasma composed of ions and electrons. By analyzing boundary layer under physically relevant condition and utilizing multi-scale asymptotic expansion method, we derive the boundary layer equations and construct the approximate solutions. Then, we use the energy estimate to give the linear stability of the approximate solutions. (C) 2022 Elsevier Inc. All rights reserved.
Keyword ：
Navier-slip boundary conditions Navier-slip boundary conditions Quasi-neutral limit Quasi-neutral limit Boundary layer Boundary layer Two-fluid Navier-Stokes-Poisson equations Two-fluid Navier-Stokes-Poisson equations Zero-viscosity limit Zero-viscosity limit
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| GB/T 7714 | Yu, Tiantian , Li, Yong . Boundary layer problem and combined limits of the two-fluid Navier-Stokes-Poisson system [J]. | JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS , 2022 , 512 (1) . |
| MLA | Yu, Tiantian 等. "Boundary layer problem and combined limits of the two-fluid Navier-Stokes-Poisson system" . | JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 512 . 1 (2022) . |
| APA | Yu, Tiantian , Li, Yong . Boundary layer problem and combined limits of the two-fluid Navier-Stokes-Poisson system . | JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS , 2022 , 512 (1) . |
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Abstract ：
This paper is concerned with the stability of traveling waves for a Keller-Segel model with singular chemotactic term and zero chemo-attractant diffusion, where the model and the waves are established to explain the propagation of bacteria pulses along a capillary tube observed in Adler's experiment [1]. By applying the detailed spectral analysis, Evans function method and special transformations and combining with some numerical simulations, in some range of the parameters all the waves are shown to be spectrally stable in some exponentially weighted spaces, and in other range of parameters all the waves are shown to be unstable in any exponentially weighted spaces. The local well-posedness of the classical positive solution to the Cauchy problem of the model is also obtained by applying semigroup argument and some special transformations. (c) 2021 Elsevier Inc. All rights reserved.
Keyword ：
Stability Stability Evans function Evans function Traveling waves Traveling waves Spectral analysis Spectral analysis Chemotactic model Chemotactic model
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| GB/T 7714 | Li, Yi , Li, Yong , Wu, Yaping et al. Spectral stability of bacteria pulses for a Keller-Segel chemotactic model [J]. | JOURNAL OF DIFFERENTIAL EQUATIONS , 2021 , 304 : 229-286 . |
| MLA | Li, Yi et al. "Spectral stability of bacteria pulses for a Keller-Segel chemotactic model" . | JOURNAL OF DIFFERENTIAL EQUATIONS 304 (2021) : 229-286 . |
| APA | Li, Yi , Li, Yong , Wu, Yaping , Zhang, Hao . Spectral stability of bacteria pulses for a Keller-Segel chemotactic model . | JOURNAL OF DIFFERENTIAL EQUATIONS , 2021 , 304 , 229-286 . |
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Abstract ：
The quasineutral limit of the isothermal Navier-Stokes-Poisson system is rigorously proved when the combined quasineutral and vanishing viscosity limit is considered in a domain with boundary. The convergence of the global weak solution for Navier-Stokes-Poisson system to the strong solution for incompressible Euler equations is obtained. (C) 2021 Elsevier Ltd. All rights reserved.
Keyword ：
Incompressible Euler equations Incompressible Euler equations Navier-Stokes-Poisson Navier-Stokes-Poisson Boundary layer Boundary layer Quasineutral limit Quasineutral limit
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| GB/T 7714 | Ju, Qiangchang , Li, Yong , Yu, Tiantian . Quasi-neutral limit of the Isothermal Naiver-Stokes-Poisson with boundary [J]. | APPLIED MATHEMATICS LETTERS , 2021 , 121 . |
| MLA | Ju, Qiangchang et al. "Quasi-neutral limit of the Isothermal Naiver-Stokes-Poisson with boundary" . | APPLIED MATHEMATICS LETTERS 121 (2021) . |
| APA | Ju, Qiangchang , Li, Yong , Yu, Tiantian . Quasi-neutral limit of the Isothermal Naiver-Stokes-Poisson with boundary . | APPLIED MATHEMATICS LETTERS , 2021 , 121 . |
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Abstract ：
The quasineutral limit of the two-fluid Euler-Poisson system (one for ions and another for electrons) in a bounded domain of R-3 is rigorously proved by investigating the existence and the stability of boundary layers. The non-penetration boundary condition for velocities and Dirichlet boundary condition for electric potential are considered. (C) 2018 Elsevier Inc. All rights reserved.
Keyword ：
Two-fluid Euler-Poisson system Two-fluid Euler-Poisson system Quasineutral limit Quasineutral limit Boundary layer Boundary layer Compressible isothermal Euler equations Compressible isothermal Euler equations
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| GB/T 7714 | Ju, Qiangchang , Li, Yong . Quasineutral limit of the two-fluid Euler-Poisson system in a bounded domain of R-3 [J]. | JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS , 2019 , 469 (1) : 169-187 . |
| MLA | Ju, Qiangchang et al. "Quasineutral limit of the two-fluid Euler-Poisson system in a bounded domain of R-3" . | JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 469 . 1 (2019) : 169-187 . |
| APA | Ju, Qiangchang , Li, Yong . Quasineutral limit of the two-fluid Euler-Poisson system in a bounded domain of R-3 . | JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS , 2019 , 469 (1) , 169-187 . |
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Abstract ：
In this paper, we study the approximation of pi through the semiperimeter or area of a random n-sided polygon inscribed in a unit circle in R-2. We show that, with probability 1, the approximation error goes to 0 as n -> infinity, and is roughly sextupled when compared with the classical Archimedean approach of using a regular n-sided polygon. By combining both the semiperimeter and area of these random inscribed polygons, we also construct extrapolation improvements that can significantly speed up the convergence of these approximations.
Keyword ：
random polygon random polygon random division random division Borel-Cantelli lemma Borel-Cantelli lemma extrapolation extrapolation Archimedean polygon Archimedean polygon
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| GB/T 7714 | Xu, Wen-Qing , Meng, Linlin , Li, Yong . Random Polygons and Estimations of pi [J]. | OPEN MATHEMATICS , 2019 , 17 : 575-581 . |
| MLA | Xu, Wen-Qing et al. "Random Polygons and Estimations of pi" . | OPEN MATHEMATICS 17 (2019) : 575-581 . |
| APA | Xu, Wen-Qing , Meng, Linlin , Li, Yong . Random Polygons and Estimations of pi . | OPEN MATHEMATICS , 2019 , 17 , 575-581 . |
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Abstract ：
In this paper, we consider the compressible quantum Navier-Stokes-Poisson equations with a linear density-dependent viscosity. By the use of a singular pressure close to vacuum, we prove the global-in-time existence of weak solutions in a three-dimensional torus for large data in the sense of distribution. Published by AIP
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| GB/T 7714 | Yang, Jianwei , Li, Yong . Global existence of weak solution for quantum Navier-Stokes-Poisson equations [J]. | JOURNAL OF MATHEMATICAL PHYSICS , 2017 , 58 (7) . |
| MLA | Yang, Jianwei et al. "Global existence of weak solution for quantum Navier-Stokes-Poisson equations" . | JOURNAL OF MATHEMATICAL PHYSICS 58 . 7 (2017) . |
| APA | Yang, Jianwei , Li, Yong . Global existence of weak solution for quantum Navier-Stokes-Poisson equations . | JOURNAL OF MATHEMATICAL PHYSICS , 2017 , 58 (7) . |
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