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学者姓名：王伟伟
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Abstract ：
Recently, Li–Fu–Wang (Li et al., 2022) established the optimal temporal decay rates of solutions near the equilibrium state to the 3D compressible magnetohydrodynamic system with nonlinear damping αuβ−1u for β⩾3. In this paper, we further extend Li–Fu–Wang's result to the case β>1 by finer energy estimates. © 2024
Keyword ：
Damping Damping Decay (organic) Decay (organic) Magnetohydrodynamics Magnetohydrodynamics
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| GB/T 7714 | Zeng, Ruixin , Fu, Shengbin , Wang, Weiwei . Optimal temporal decay rates for 3D compressible magnetohydrodynamics system with nonlinear damping [J]. | Applied Mathematics Letters , 2024 , 156 . |
| MLA | Zeng, Ruixin 等. "Optimal temporal decay rates for 3D compressible magnetohydrodynamics system with nonlinear damping" . | Applied Mathematics Letters 156 (2024) . |
| APA | Zeng, Ruixin , Fu, Shengbin , Wang, Weiwei . Optimal temporal decay rates for 3D compressible magnetohydrodynamics system with nonlinear damping . | Applied Mathematics Letters , 2024 , 156 . |
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Abstract ：
Recently, Li-Fu-Wang (Li et al., 2022) established the optimal temporal decay rates of solutions near the equilibrium state to the 3D compressible magnetohydrodynamic system with nonlinear damping alpha|u|(beta-1)u for beta >= 3. In this paper, we further extend Li-Fu-Wang's result to the case beta > 1 by finer energy estimates.
Keyword ：
Compressible magnetohydrodynamic fluids Compressible magnetohydrodynamic fluids Global-in-time existence Global-in-time existence Nonlinear damping Nonlinear damping Optimal time-decay rates Optimal time-decay rates Uniqueness Uniqueness
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| GB/T 7714 | Zeng, Ruixin , Fu, Shengbin , Wang, Weiwei . Optimal temporal decay rates for 3D compressible magnetohydrodynamics system with nonlinear damping [J]. | APPLIED MATHEMATICS LETTERS , 2024 , 156 . |
| MLA | Zeng, Ruixin 等. "Optimal temporal decay rates for 3D compressible magnetohydrodynamics system with nonlinear damping" . | APPLIED MATHEMATICS LETTERS 156 (2024) . |
| APA | Zeng, Ruixin , Fu, Shengbin , Wang, Weiwei . Optimal temporal decay rates for 3D compressible magnetohydrodynamics system with nonlinear damping . | APPLIED MATHEMATICS LETTERS , 2024 , 156 . |
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This paper investigates the temporal decay rates of solutions to the Cauchy problem of a model, which describes the combustion of the compressible fluid. Suppose that the initial data is a small perturbation near the equilibrium state (rho(infinity),0,theta(infinity),zeta), where rho(infinity)>0, theta(infinity)theta I discussed in Wang and Wen (Sci China Math 65:1199-1228 (2022).
Keyword ：
Compressible combustion fluids Compressible combustion fluids Energy estimates Energy estimates Global strong solutions Global strong solutions Optimal temporal decay rates Optimal temporal decay rates
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| GB/T 7714 | Fu, Shengbin , Huang, Wenting , Wang, Weiwei . Optimal temporal decay rates of solutions for combustion of compressible fluids [J]. | ANALYSIS AND MATHEMATICAL PHYSICS , 2024 , 14 (6) . |
| MLA | Fu, Shengbin 等. "Optimal temporal decay rates of solutions for combustion of compressible fluids" . | ANALYSIS AND MATHEMATICAL PHYSICS 14 . 6 (2024) . |
| APA | Fu, Shengbin , Huang, Wenting , Wang, Weiwei . Optimal temporal decay rates of solutions for combustion of compressible fluids . | ANALYSIS AND MATHEMATICAL PHYSICS , 2024 , 14 (6) . |
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The stability and large-time behavior problem on the magneto-micropolar equations has evoked a considerable interest in recent years. In this paper, we study the stability and exponential decay near magnetic hydrostatic equilibrium to the two-dimensional magneto-micropolar equations with partial dissipation in the domain O= T x R. In particular, we takes advantage of the geometry of the domain T x R to divide u into zeroth mode and the nonzero modes, and obey a strong version of the Poincare's inequality, which plays a crucial role in controlling the nonlinearity. Moreover, we find that the oscillation part of the solution decays exponentially to zero. Finally, our result mathematically verifies that the stabilization effect of a background magnetic field on magneto-micropolar fluids.
Keyword ：
large-time behavior large-time behavior Magneto-micropolar fluids Magneto-micropolar fluids partial dissipation partial dissipation stability stability
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| GB/T 7714 | Zhang, Yajie , Wang, Weiwei . Stability and exponential decay for the 2D magneto-micropolar equations with partial dissipation [J]. | APPLICABLE ANALYSIS , 2023 , 103 (2) : 432-444 . |
| MLA | Zhang, Yajie 等. "Stability and exponential decay for the 2D magneto-micropolar equations with partial dissipation" . | APPLICABLE ANALYSIS 103 . 2 (2023) : 432-444 . |
| APA | Zhang, Yajie , Wang, Weiwei . Stability and exponential decay for the 2D magneto-micropolar equations with partial dissipation . | APPLICABLE ANALYSIS , 2023 , 103 (2) , 432-444 . |
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In this paper, we focus on Cauchy problem of the non-isentropic compressible Navier-Stokes-Poisson system with the initial perturbation (& rho;0-& rho; over bar ,m0,& theta;0-& theta; over bar )$$ \left({\rho} circumflex 0-\overline{\rho},{\mathbf{m}} circumflex 0,{\theta} circumflex 0-\overline{\theta}\right) $$ belonging to the space Hl(Double-struck capital R3)& AND;B1,& INFIN;-s(Double-struck capital R3)$$ {H} circumflex l\left({\mathrm{\mathbb{R}}} circumflex 3\right)\cap {\dot{B}}_{1,\infty} circumflex {-s}\left({\mathrm{\mathbb{R}}} circumflex 3\right) $$, where l & GT;4$$ l\geqslant 4 $$ and s & ISIN;[0,1]$$ s\in \left[0,1\right] $$. More importantly, we establish the optimal temporal decay rate of the global strong solution, which can be considered as further work.
Keyword ：
Besov spaces Besov spaces Navier-Stokes-Poisson system Navier-Stokes-Poisson system optimal decay rates optimal decay rates
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| GB/T 7714 | Fu, Shengbin , Wang, Weiwei . Optimal temporal decay rate of the non-isentropic compressible Navier-Stokes-Poisson system [J]. | MATHEMATICAL METHODS IN THE APPLIED SCIENCES , 2023 , 47 (2) : 986-1014 . |
| MLA | Fu, Shengbin 等. "Optimal temporal decay rate of the non-isentropic compressible Navier-Stokes-Poisson system" . | MATHEMATICAL METHODS IN THE APPLIED SCIENCES 47 . 2 (2023) : 986-1014 . |
| APA | Fu, Shengbin , Wang, Weiwei . Optimal temporal decay rate of the non-isentropic compressible Navier-Stokes-Poisson system . | MATHEMATICAL METHODS IN THE APPLIED SCIENCES , 2023 , 47 (2) , 986-1014 . |
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In this paper, we are interested in the global well-posedness of the strong solutions to the Cauchy problem on the compressible magnetohydrodynamics system with Hall effect. Moreover, we establish the convergence rates of the above solutions trending towards the constant equilibrium (& rho; over bar ,0,B over bar )\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$({\bar{\rho }},0,\bar{\textbf{B}})$$\end{document}, provided that the initial perturbation belonging to H3(R3)& AND;B2,& INFIN;-s(R3)\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$H<^>3({\mathbb {R}}<^>3) \cap B_{2, \infty }<^>{-s}({\mathbb {R}}<^>3)$$\end{document} for s & ISIN;(0,32]\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$s \in (0,\frac{3}{2}]$$\end{document} is sufficiently small.
Keyword ：
Compressible Hall-magnetohydrodynamics system Compressible Hall-magnetohydrodynamics system Fixed point theorem Fixed point theorem Optimal temporal decay rates Optimal temporal decay rates Pure energy methods Pure energy methods
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| GB/T 7714 | Fu, Shengbin , Wang, Weiwei . The Optimal Temporal Decay Rates for Compressible Hall-magnetohydrodynamics System [J]. | JOURNAL OF MATHEMATICAL FLUID MECHANICS , 2023 , 25 (4) . |
| MLA | Fu, Shengbin 等. "The Optimal Temporal Decay Rates for Compressible Hall-magnetohydrodynamics System" . | JOURNAL OF MATHEMATICAL FLUID MECHANICS 25 . 4 (2023) . |
| APA | Fu, Shengbin , Wang, Weiwei . The Optimal Temporal Decay Rates for Compressible Hall-magnetohydrodynamics System . | JOURNAL OF MATHEMATICAL FLUID MECHANICS , 2023 , 25 (4) . |
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This paper focuses on the Rayleigh-Taylor instability in the two-dimensional system of equations of nonhomogeneous incompressible viscous fluids with capillarity effects in a horizontal periodic domain with infinite height. First, we use the modified variational method to construct (linear) unstable solutions for the linearized capillary Rayleigh-Taylor problem. Then, motivated by the Grenier's idea in (Grenier in Commun. Pure Appl. Math. 53(9):1067-1091, 2000), we further construct approximate solutions with higher-order growing modes to the capillary Rayleigh-Taylor problem and derive the error estimates between both the approximate solutions and nonlinear solutions of the capillary Rayleigh-Taylor problem. Finally, we prove the existence of escape points based on the bootstrap instability method of Hwang-Guo in (Hwang and Guo in Arch. Ration. Mech. Anal. 167(3):235-253, 2003), and thus obtain the nonlinear Rayleigh-Taylor instability result. Our instability result presents that the Rayleigh-Taylor instability can occur in the fluids with capillarity effects for any capillary coefficient ? > 0 if the critical capillary coefficient is infinite. In particular, it improves the previous Zhang's result in (Zhang in J. Math. Fluid Mech. 24(3):70-23, 2022) with the assumption of smallness of the capillary coefficient.
Keyword ：
Incompressible Navier-Stokes-Korteweg equations Incompressible Navier-Stokes-Korteweg equations Incompressible viscous fluids with capillarity effects Incompressible viscous fluids with capillarity effects Rayleigh-Taylor instability Rayleigh-Taylor instability
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| GB/T 7714 | Zhang, Xuyan , Tian, Fangfang , Wang, Weiwei . On Rayleigh-Taylor instability in Navier-Stokes-Korteweg equations [J]. | JOURNAL OF INEQUALITIES AND APPLICATIONS , 2023 , 2023 (1) . |
| MLA | Zhang, Xuyan 等. "On Rayleigh-Taylor instability in Navier-Stokes-Korteweg equations" . | JOURNAL OF INEQUALITIES AND APPLICATIONS 2023 . 1 (2023) . |
| APA | Zhang, Xuyan , Tian, Fangfang , Wang, Weiwei . On Rayleigh-Taylor instability in Navier-Stokes-Korteweg equations . | JOURNAL OF INEQUALITIES AND APPLICATIONS , 2023 , 2023 (1) . |
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For the Cauchy problem of the three-dimensional compressible viscoelastic flows, we establish the optimal temporal decay rates of the all-order spatial derivatives of the global strong solution in the weaker initial condition. The main novelty of this paper is that the optimal decay estimates of the highest-order derivatives of the solution is obtained by using spectral analysis and energy method, which can be considered as the further investigation to [X. Hu and G. Wu, Global existence and optimal decay rates for three-dimensional compressible viscoelastic flows, SIAM J. Math. Anal. 45 (2013) 2815-2833] with only the lower-order derivative estimates.
Keyword ：
all-order derivatives all-order derivatives optimal temporal decay estimates optimal temporal decay estimates Viscoelastic flows Viscoelastic flows
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| GB/T 7714 | Fu, Shengbin , Huang, Wenting , Wang, Weiwei . Optimal temporal decay rates for the compressible viscoelastic flows [J]. | ANALYSIS AND APPLICATIONS , 2023 , 21 (05) : 1365-1389 . |
| MLA | Fu, Shengbin 等. "Optimal temporal decay rates for the compressible viscoelastic flows" . | ANALYSIS AND APPLICATIONS 21 . 05 (2023) : 1365-1389 . |
| APA | Fu, Shengbin , Huang, Wenting , Wang, Weiwei . Optimal temporal decay rates for the compressible viscoelastic flows . | ANALYSIS AND APPLICATIONS , 2023 , 21 (05) , 1365-1389 . |
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Recently, Hattori-Lagha established the global existence and asymptotic behavior of the solutions for a three-dimensional compressible chemotaxis system with chemoattractant and repellent (Hattori and Lagha in Discrete Contin. Dyn. Syst. 41(11):5141-5164, 2021). Motivated by Hattori-Lagha's work, we further investigated the optimal time-decay rates of strong solutions with small perturbation to the three-dimensional Keller-Segel system coupled to the compressible Navier-Stokes equations, which models for the motion of swimming bacteria in a compressible viscous fluid. First, we reformulate the system into a perturbation form. Then we establish a prior estimates of solutions and prove the existence of the global-in-time solutions based on the local existence of unique solutions. Finally, we will establish the optimal time-decay rates of the nonhomogeneous system by the decomposition technique of both low and high frequencies of solutions as in (Wang and Wen in Sci. China Math., 2020, https://doi.org/10.1007/s11425-020-1779-7). Moreover, the decay rate is optimal since it agrees with the solutions of the linearized system.
Keyword ：
Compressible chemotactic fluids Compressible chemotactic fluids Fourier theory Fourier theory Global existence Global existence Optimal time-decay rates Optimal time-decay rates Uniqueness Uniqueness
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| GB/T 7714 | Guo, Yuting , Sun, Rui , Wang, Weiwei . Optimal time-decay rates of the Keller-Segel system coupled to compressible Navier-Stokes equation in three dimensions [J]. | BOUNDARY VALUE PROBLEMS , 2022 , 2022 (1) . |
| MLA | Guo, Yuting 等. "Optimal time-decay rates of the Keller-Segel system coupled to compressible Navier-Stokes equation in three dimensions" . | BOUNDARY VALUE PROBLEMS 2022 . 1 (2022) . |
| APA | Guo, Yuting , Sun, Rui , Wang, Weiwei . Optimal time-decay rates of the Keller-Segel system coupled to compressible Navier-Stokes equation in three dimensions . | BOUNDARY VALUE PROBLEMS , 2022 , 2022 (1) . |
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Recently, Gao and Yao established the global existence and temporal decay rates of solutions for a system of compressible Hall-magnetohydrodynamic fluids (Gao and Yao in Discrete Contin. Dyn. Syst. 36: 3077-3106, 2016). However, because of the difficulty of derivative loss in the nonlinear terms, Gao and Yao could not provide the temporal decay for the highest-order derivatives of classical solutions. In this paper, motivated by the decomposition technique of both low and high frequencies of solutions in (Wang and Wen in Sci. China Math. 65: 1199-1228 2022), we further derive the temporal decay for the highest-order derivatives of the strong solutions. Moreover, the decay rate is optimal, since it agrees with the solutions of the linearized system.
Keyword ：
Compressible Hall-magnetohydrodynamic fluids Compressible Hall-magnetohydrodynamic fluids Fourier theory Fourier theory Highest-order derivatives Highest-order derivatives Optimal time-decay rates Optimal time-decay rates
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| GB/T 7714 | Sun, Rui , Guo, Yuting , Wang, Weiwei . Temporal decay for the highest-order derivatives of solutions of the compressible Hall-magnetohydrodynamic equations [J]. | BOUNDARY VALUE PROBLEMS , 2022 , 2022 (1) . |
| MLA | Sun, Rui 等. "Temporal decay for the highest-order derivatives of solutions of the compressible Hall-magnetohydrodynamic equations" . | BOUNDARY VALUE PROBLEMS 2022 . 1 (2022) . |
| APA | Sun, Rui , Guo, Yuting , Wang, Weiwei . Temporal decay for the highest-order derivatives of solutions of the compressible Hall-magnetohydrodynamic equations . | BOUNDARY VALUE PROBLEMS , 2022 , 2022 (1) . |
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