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学者姓名：王术
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Abstract ：
In this paper, we are concerned with the conservation of energy criterion of the weak solutions to the Navier-Stokes-Fourier equations on the torus allowing vacuum. We establish the energy conservation criteria via the gradient of velocity for the weak solutions of this system, which generalizes the corresponding recent energy conservation criteria in terms of the velocity obtained by Aoki and Iwabuchi in Aoki and Iwabuchi (2022). Moreover, sufficient conditions for weak solutions keeping the energy balance allowing vacuum are shown for the full Navier-Stokes equations.
Keyword ：
Weak solutions Weak solutions Vacuum Vacuum Full Navier-Stokes equations Full Navier-Stokes equations Energy equality Energy equality
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| GB/T 7714 | Ji, Xiang , Wang, Shu , Zhang, Jie . Energy equality of weak solutions of the Navier-Stokes-Fourier equations allowing vacuum [J]. | NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS , 2024 , 77 . |
| MLA | Ji, Xiang 等. "Energy equality of weak solutions of the Navier-Stokes-Fourier equations allowing vacuum" . | NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS 77 (2024) . |
| APA | Ji, Xiang , Wang, Shu , Zhang, Jie . Energy equality of weak solutions of the Navier-Stokes-Fourier equations allowing vacuum . | NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS , 2024 , 77 . |
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Abstract ：
We consider non-isentropic Euler-Maxwell equations with relaxation times (small physical parameters) arising in the models of magnetized plasma and semiconductors. For smooth periodic initial data sufficiently close to constant steady-states, we prove the uniformly global existence of smooth solutions with respect to the parameter, and the solutions converge global-in-time to the solutions of the energy-transport equations in a slow time scaling as the relaxation time goes to zero. We also establish error estimates between the smooth periodic solutions of the non-isentropic Euler-Maxwell equations and those of energy-transport equations. The proof is based on stream function techniques and the classical energy method but with some new developments. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
Keyword ：
Convergence rates Convergence rates Non-isentropic Euler-Maxwell equations Non-isentropic Euler-Maxwell equations Energy-transport equations Energy-transport equations Stream function Stream function
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| GB/T 7714 | Feng, Yue-Hong , Li, Rui , Mei, Ming et al. Global convergence rates in zero-relaxation limits for non-isentropic Euler-Maxwell equations [J]. | JOURNAL OF DIFFERENTIAL EQUATIONS , 2024 , 414 : 372-404 . |
| MLA | Feng, Yue-Hong et al. "Global convergence rates in zero-relaxation limits for non-isentropic Euler-Maxwell equations" . | JOURNAL OF DIFFERENTIAL EQUATIONS 414 (2024) : 372-404 . |
| APA | Feng, Yue-Hong , Li, Rui , Mei, Ming , Wang, Shu . Global convergence rates in zero-relaxation limits for non-isentropic Euler-Maxwell equations . | JOURNAL OF DIFFERENTIAL EQUATIONS , 2024 , 414 , 372-404 . |
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Abstract ：
In this note, we investigate steady compressible nematic liquid crystal flows in Double-struck capital R3$$ {\mathrm{\mathbb{R}}} circumflex 3 $$. We establish Liouville-type theorems for smooth solutions (rho,u,d)$$ \left(\rho, u,d\right) $$ that fulfill specific conditions within Lorentz spaces.
Keyword ：
Lorentz space Lorentz space stationary nematic liquid crystal equations stationary nematic liquid crystal equations Liouville-type theorems Liouville-type theorems
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| GB/T 7714 | Zhang, Jie , Wang, Shu , Ji, Xiang . Notes on Liouville-type theorems for the 3D compressible nematic liquid crystal equations [J]. | MATHEMATICAL METHODS IN THE APPLIED SCIENCES , 2024 , 47 (8) : 7046-7055 . |
| MLA | Zhang, Jie et al. "Notes on Liouville-type theorems for the 3D compressible nematic liquid crystal equations" . | MATHEMATICAL METHODS IN THE APPLIED SCIENCES 47 . 8 (2024) : 7046-7055 . |
| APA | Zhang, Jie , Wang, Shu , Ji, Xiang . Notes on Liouville-type theorems for the 3D compressible nematic liquid crystal equations . | MATHEMATICAL METHODS IN THE APPLIED SCIENCES , 2024 , 47 (8) , 7046-7055 . |
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Abstract ：
In this note, we study the steady incompressible nematic liquid crystal flows in R-3. We establish the anisotropic Liouville-type theorems when a smooth solution (u, d) satisfies some suitable conditions.
Keyword ：
Liouville-type theorem Liouville-type theorem Stationary incompressible nematic liquid crystal equations Stationary incompressible nematic liquid crystal equations
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| GB/T 7714 | Zhang, Jie , Wang, Shu . Notes on Anisotropic Liouville-type Theorems for 3D Stationary Nematic Liquid Crystal Equations [J]. | BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY , 2023 , 46 (6) . |
| MLA | Zhang, Jie et al. "Notes on Anisotropic Liouville-type Theorems for 3D Stationary Nematic Liquid Crystal Equations" . | BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY 46 . 6 (2023) . |
| APA | Zhang, Jie , Wang, Shu . Notes on Anisotropic Liouville-type Theorems for 3D Stationary Nematic Liquid Crystal Equations . | BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY , 2023 , 46 (6) . |
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Abstract ：
In this paper we consider the initial value problem to the fractional compressible isentropic generalized Navier-Stokes equations for viscous fluids with one Levy diffusion process in which the viscosity term appeared in the fluid equations is described by the nonlocal fractional Laplace operator. We give one detailed spectrum analysis on a linearized operator and the decay law in time of the solution semigroup for the linearized fractional compressible isentropic generalized Navier-Stokes equations around a constant state by the Fourier analysis technique, which is shown that the order of the fractional derivatives plays a key role in the analysis so that the spectrum structure involved here is more complex than that of the classical compressible Navier-Stokes system. Based on this and the elaborate energy method, the global-in-time existence and one optimal decay rate in time of the smooth solution are obtained under the assumption that the initial data are given in a small neighborhood of a constant state. (c) 2023 Elsevier Inc. All rights reserved.
Keyword ：
Optimal decay rate Optimal decay rate diffusion process diffusion process Global-in-time existence Global-in-time existence Fractional compressible generalized Navier-Stokes equation Fractional compressible generalized Navier-Stokes equation
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| GB/T 7714 | Wang, Shu , Zhang, Shuzhen . The initial value problem for the equations of motion of fractional compressible viscous fluids [J]. | JOURNAL OF DIFFERENTIAL EQUATIONS , 2023 , 377 : 369-417 . |
| MLA | Wang, Shu et al. "The initial value problem for the equations of motion of fractional compressible viscous fluids" . | JOURNAL OF DIFFERENTIAL EQUATIONS 377 (2023) : 369-417 . |
| APA | Wang, Shu , Zhang, Shuzhen . The initial value problem for the equations of motion of fractional compressible viscous fluids . | JOURNAL OF DIFFERENTIAL EQUATIONS , 2023 , 377 , 369-417 . |
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Abstract ：
This paper is concerned with the zero-relaxation limits for periodic smooth solutions of the non-isentropic Euler-Maxwell system in a three-dimensional torus prescribing the well/ill-prepared initial data. The non-isentropic Euler-Maxwell system can be reduced to a quasi-linear symmetric hyperbolic system of one order. By observing a special structure of the non-isentropic Euler-Maxwell system, we are able to decouple the system and develop a technique to achieve the a priori H-S estimates, which guarantees the limit for the non-isentropic Euler-Maxwell system as the relaxation time tau -> 0. We realize that the convergence rate of the temperature is the same as the other unknowns in the L-infinity(0, T-1; H-S), but the convergence rate of the temperature is slower than the velocity in L-2(0, T-1; H-S). The zero-relaxation limit presented here is the transport equation coupled with the drift-diffusion system. However, the limit of the isentropic Euler-Maxwell system is the classical drift-diffusion system. This shows the essential difference between the isentropic and non-isentropic Euler-Maxwell systems.
Keyword ：
Initial layer problem Initial layer problem Zero-relaxation limits Zero-relaxation limits The non-isentropic Euler-Maxwell system The non-isentropic Euler-Maxwell system
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| GB/T 7714 | Feng, Yue-Hong , Li, Xin , Mei, Ming et al. Zero-Relaxation Limits of the Non-Isentropic Euler-Maxwell System for Well/Ill-Prepared Initial Data [J]. | JOURNAL OF NONLINEAR SCIENCE , 2023 , 33 (5) . |
| MLA | Feng, Yue-Hong et al. "Zero-Relaxation Limits of the Non-Isentropic Euler-Maxwell System for Well/Ill-Prepared Initial Data" . | JOURNAL OF NONLINEAR SCIENCE 33 . 5 (2023) . |
| APA | Feng, Yue-Hong , Li, Xin , Mei, Ming , Wang, Shu . Zero-Relaxation Limits of the Non-Isentropic Euler-Maxwell System for Well/Ill-Prepared Initial Data . | JOURNAL OF NONLINEAR SCIENCE , 2023 , 33 (5) . |
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Abstract ：
We consider the initial value problem to the fractional system of motions for compressible viscous fluids in this paper. We establish a local well-posedness theory for the system, as well as a global well-posedness theory for small initial data. We also show the large-time behavior of the solution, where solutions converge to a constant steady state exponentially in time.& COPY;2023 Elsevier Ltd. All rights reserved.
Keyword ：
Optimal decay rate Optimal decay rate Global-in-time existence Global-in-time existence Fractional Navier-Stokes equation Fractional Navier-Stokes equation
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| GB/T 7714 | Wang, Shu , Zhang, Shuzhen . The global classical solution to compressible system with fractional viscous term [J]. | NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS , 2023 , 75 . |
| MLA | Wang, Shu et al. "The global classical solution to compressible system with fractional viscous term" . | NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS 75 (2023) . |
| APA | Wang, Shu , Zhang, Shuzhen . The global classical solution to compressible system with fractional viscous term . | NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS , 2023 , 75 . |
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Abstract ：
The global well-posedness of a new class of initial-boundary value problem on incompressible MHD equations in the bounded domain with the smooth boundary is studied. The existence of a class of global weak solution to the initial boundary value problem for two/three-dimensional incompressible MHD equa-tion with the given pressure-velocity's relation boundary condition for the fluid field at the boundary and with one perfectly insulating boundary condition for the magnetic field at the boundary is obtained, and the global existence and uniqueness of the smooth solution to the corresponding problem in two-dimensional case for the smooth initial data is also established. The corresponding results are also extended to the two/three-dimensional incompressible MHD-Boussinesq equations with the density-velocity's rela-tion boundary condition for the density.(c) 2023 Elsevier Inc. All rights reserved.
Keyword ：
MHD-Boussinesq equations MHD-Boussinesq equations Incompressible MHD Incompressible MHD Global smooth solution Global smooth solution Global weak solution Global weak solution
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| GB/T 7714 | Wang, Shu . Global well-posedness of a new class of initial-boundary value problem on incompressible MHD/MHD-Boussinesq equations [J]. | JOURNAL OF DIFFERENTIAL EQUATIONS , 2023 , 363 : 465-490 . |
| MLA | Wang, Shu . "Global well-posedness of a new class of initial-boundary value problem on incompressible MHD/MHD-Boussinesq equations" . | JOURNAL OF DIFFERENTIAL EQUATIONS 363 (2023) : 465-490 . |
| APA | Wang, Shu . Global well-posedness of a new class of initial-boundary value problem on incompressible MHD/MHD-Boussinesq equations . | JOURNAL OF DIFFERENTIAL EQUATIONS , 2023 , 363 , 465-490 . |
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Abstract ：
In this paper, we consider the compressible Navier-Stokes-Maxwell equations with a non-constant background density in R-3. We first show the existence and uniqueness of the non-trivial equilibrium (steady-state) of the system when the background density is a small variation of certain constant state, then we prove the asymptotic stability of the steady-state once the initial perturbation around the steady-state is small. Furthermore, by establishing the time-decay estimates for the corresponding linearized homogeneous equations, we artfully derive the time-algebraic convergence rates. The proof is based on the time-weighted energy method but with some new developments on the weight settings.
Keyword ：
Compressible Navier-Stokes-Maxwell equations Compressible Navier-Stokes-Maxwell equations Convergence to steady-states Convergence to steady-states Time decay rates Time decay rates
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| GB/T 7714 | Feng, Yue-Hong , Li, Xin , Mei, Ming et al. Convergence to Steady-States of Compressible Navier-Stokes-Maxwell Equations [J]. | JOURNAL OF NONLINEAR SCIENCE , 2022 , 32 (1) . |
| MLA | Feng, Yue-Hong et al. "Convergence to Steady-States of Compressible Navier-Stokes-Maxwell Equations" . | JOURNAL OF NONLINEAR SCIENCE 32 . 1 (2022) . |
| APA | Feng, Yue-Hong , Li, Xin , Mei, Ming , Wang, Shu , Cao, Yang-Chen . Convergence to Steady-States of Compressible Navier-Stokes-Maxwell Equations . | JOURNAL OF NONLINEAR SCIENCE , 2022 , 32 (1) . |
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Abstract ：
Global in time weak solutions to the alpha-model regularization for the three dimensional Euler-Poisson equations are considered in this paper. We prove the existence of global weak solutions to alpha-model regularization for the three dimension compressible Euler-Poisson equations by using the Fadeo-Galerkin method and the compactness arguments on the condition that the adiabatic constant satisfies gamma > 4/3.
Keyword ：
alpha-model regularization for Euler-Poisson equations alpha-model regularization for Euler-Poisson equations Faedo-Galerkin method Faedo-Galerkin method Global weak solutions Global weak solutions
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| GB/T 7714 | Ren, Yabo , Guo, Boling , Wang, Shu . GLOBAL WEAK SOLUTIONS TO THE alpha-MODEL REGULARIZATION FOR 3D COMPRESSIBLE EULER-POISSON EQUATIONS [J]. | ACTA MATHEMATICA SCIENTIA , 2021 , 41 (3) : 679-702 . |
| MLA | Ren, Yabo et al. "GLOBAL WEAK SOLUTIONS TO THE alpha-MODEL REGULARIZATION FOR 3D COMPRESSIBLE EULER-POISSON EQUATIONS" . | ACTA MATHEMATICA SCIENTIA 41 . 3 (2021) : 679-702 . |
| APA | Ren, Yabo , Guo, Boling , Wang, Shu . GLOBAL WEAK SOLUTIONS TO THE alpha-MODEL REGULARIZATION FOR 3D COMPRESSIBLE EULER-POISSON EQUATIONS . | ACTA MATHEMATICA SCIENTIA , 2021 , 41 (3) , 679-702 . |
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