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学者姓名：王术
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摘要 ：
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.
关键词 ：
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 等. "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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摘要 ：
The initial value problems of bipolar isentropic/non-isentropic compressible Navier-Stokes-Maxwell (CNS-M) systems arising from plasmas in R-3 are studied. The main difficulty of studying the bipolar isentropic/non-isentropic CNS-M systems lies in the appearance of the electromagnetic fields satisfying the hyperbolic Maxwell equations. The large time-decay rates of global smooth solutions with small amplitude in L-q(R-3) for 2 <= q <= infinity are established. For the bipolar non-isentropic CNS-M system, the difference of velocities of two charged carriers decay at the rate (1 + t)- rate (1 + t)(-3/4+1/4q) which is faster than the rate (1+t)(-3/4+1/4q)(ln -3/+t))(1-2/q) of the bipolar isentropic CNS-M system, meanwhile, the magnetic field decay at the rate (1 + t)(-3/4+1/4q)(ln -3/+t))(1-2/q) which is slower than the rate (1 +t)- 34 + 4q 3 for the bipolar isentropic CNS-M system. The approach adopted is the classical energy method but with some new developments, where the techniques of choosing symmetrizers and the spectrum analysis on the linearized homogeneous system play the crucial roles. (C) 2021 Elsevier Inc. All rights reserved.
关键词 ：
non-isentropic CNS-M system non-isentropic CNS-M system Plasmas Plasmas The bipolar isentropic The bipolar isentropic Time-decay rates Time-decay rates
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| GB/T 7714 | Feng, Yue-Hong , Li, Xin , Mei, Ming et al. Asymptotic decay of bipolar isentropic/non-isentropic compressible Navier-Stokes-Maxwell systems [J]. | JOURNAL OF DIFFERENTIAL EQUATIONS , 2021 , 301 : 471-542 . |
| MLA | Feng, Yue-Hong et al. "Asymptotic decay of bipolar isentropic/non-isentropic compressible Navier-Stokes-Maxwell systems" . | JOURNAL OF DIFFERENTIAL EQUATIONS 301 (2021) : 471-542 . |
| APA | Feng, Yue-Hong , Li, Xin , Mei, Ming , Wang, Shu . Asymptotic decay of bipolar isentropic/non-isentropic compressible Navier-Stokes-Maxwell systems . | JOURNAL OF DIFFERENTIAL EQUATIONS , 2021 , 301 , 471-542 . |
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摘要 ：
The purpose of this paper is to study the local well-posedness problem on the magnetohydrodynamics (MHD)-structure interaction (MHDSI) systems. The fluid is represented by the incompressible viscous and non-resistive MHD equation in Euler coordinates while the structure is modeled by the elasticity equation with superconductor material in Lagrangian coordinates. The equations are coupled along the moving interface though transmission boundary conditions for velocity, stress and magnetic field. The local existence of at least one strong solution in time to the incompressible viscous and non-resistive MHD-structure interaction model was proved in the sense of one suitable Sobolev's space norm by using the careful energy method and fixed point theory combining with penalization and regularization techniques and by overcoming the coupling difficulties caused by the magnetic field. (C) 2020 Elsevier Inc. All rights reserved.
关键词 ：
Moving interface Moving interface Local strong solutions Local strong solutions Magnetohydrodynamics equation Magnetohydrodynamics equation Elasticity equation Elasticity equation Magnetohydrodynamics-structure interaction Magnetohydrodynamics-structure interaction
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| GB/T 7714 | Shen, Lin , Wang, Shu , Yang, Rong . Existence of local strong solutions for the incompressible viscous and non-resistive MHD-structure interaction model [J]. | JOURNAL OF DIFFERENTIAL EQUATIONS , 2021 , 272 : 473-543 . |
| MLA | Shen, Lin et al. "Existence of local strong solutions for the incompressible viscous and non-resistive MHD-structure interaction model" . | JOURNAL OF DIFFERENTIAL EQUATIONS 272 (2021) : 473-543 . |
| APA | Shen, Lin , Wang, Shu , Yang, Rong . Existence of local strong solutions for the incompressible viscous and non-resistive MHD-structure interaction model . | JOURNAL OF DIFFERENTIAL EQUATIONS , 2021 , 272 , 473-543 . |
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摘要 ：
In this article we study quasi-neutral limit and the initial layer problem of the drift-diffusion model. Different from others studies, we consider the physical case that the mobilities of the charges are different. The quasi-neutral limit with an initial layer structure is rigorously proved by using the weighted energy method coupled with multi-scaling asymptotic expansions.
关键词 ：
initial layer initial layer multiple scaling asymptotic expansions multiple scaling asymptotic expansions weighted energy functional weighted energy functional
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| GB/T 7714 | Wang, Shu , Jiang, Limin . Quasi-neutral limit and the initial layer problem of the drift-diffusion model [J]. | ACTA MATHEMATICA SCIENTIA , 2020 , 40 (4) : 1152-1170 . |
| MLA | Wang, Shu et al. "Quasi-neutral limit and the initial layer problem of the drift-diffusion model" . | ACTA MATHEMATICA SCIENTIA 40 . 4 (2020) : 1152-1170 . |
| APA | Wang, Shu , Jiang, Limin . Quasi-neutral limit and the initial layer problem of the drift-diffusion model . | ACTA MATHEMATICA SCIENTIA , 2020 , 40 (4) , 1152-1170 . |
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摘要 ：
This article concerns the initial-boundary layer effects of the 3-D incompressible Boussinesq system for Rayleigh-Benard convection with ill-prepared initial data. We consider a non-slip boundary condition for the velocity field and inhomogeneous Dirichlet boundary condition for the temperature. By means of multi-scale analysis and matched asymptotic expansion methods, we establish an accurate approximating solution for the viscous and diffusive Boussinesq system. We also study the convergence of the infinite Prandtl number limit.
关键词 ：
asymptotic expansion asymptotic expansion Boussinesq system Boussinesq system infinite Prandtl number limit infinite Prandtl number limit initial-boundary layer initial-boundary layer Rayleigh-Benard convection Rayleigh-Benard convection
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| GB/T 7714 | Fan, Xiaoting , Wang, Shu , Xu, Wen-Qing . INITIAL-BOUNDARY LAYER ASSOCIATED WITH THE 3-D BOUSSINESQ SYSTEM FOR RAYLEIGH-BENARD CONVECTION [J]. | ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS , 2020 . |
| MLA | Fan, Xiaoting et al. "INITIAL-BOUNDARY LAYER ASSOCIATED WITH THE 3-D BOUSSINESQ SYSTEM FOR RAYLEIGH-BENARD CONVECTION" . | ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS (2020) . |
| APA | Fan, Xiaoting , Wang, Shu , Xu, Wen-Qing . INITIAL-BOUNDARY LAYER ASSOCIATED WITH THE 3-D BOUSSINESQ SYSTEM FOR RAYLEIGH-BENARD CONVECTION . | ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS , 2020 . |
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摘要 ：
In this paper, we study the quasi-neutral limit for the compressible two-fluid Euler-Maxwell equations for well-prepared initial data. Precisely, we proved the solution of the three-dimensional compressible two-fluid Euler-Maxwell equations converges locally in time to that of the compressible Euler equation as E tends to zero. This proof is based on the formal asymptotic expansions, the iteration techniques, the vector analysis formulas and the Sobolev energy estimates.
关键词 ：
formal asymptotic expansions formal asymptotic expansions quasi-neutral limit quasi-neutral limit singular perturbation methods singular perturbation methods Two-fluid Euler-Maxwell equations Two-fluid Euler-Maxwell equations uniform energy estimates uniform energy estimates
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| GB/T 7714 | Li, Min , Pu, Xueke , Wang, Shu . QUASINEUTRAL LIMIT FOR THE COMPRESSIBLE TWO-FLUID EULER-MAXWELL EQUATIONS FOR WELL-PREPARED INITIAL DATA [J]. | ELECTRONIC RESEARCH ARCHIVE , 2020 , 28 (2) : 879-895 . |
| MLA | Li, Min et al. "QUASINEUTRAL LIMIT FOR THE COMPRESSIBLE TWO-FLUID EULER-MAXWELL EQUATIONS FOR WELL-PREPARED INITIAL DATA" . | ELECTRONIC RESEARCH ARCHIVE 28 . 2 (2020) : 879-895 . |
| APA | Li, Min , Pu, Xueke , Wang, Shu . QUASINEUTRAL LIMIT FOR THE COMPRESSIBLE TWO-FLUID EULER-MAXWELL EQUATIONS FOR WELL-PREPARED INITIAL DATA . | ELECTRONIC RESEARCH ARCHIVE , 2020 , 28 (2) , 879-895 . |
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摘要 ：
This paper investigates the globally dynamical stabilizing effects of the geometry of the domain at which the flow locates and of the geometry structure of the solutions with the finite energy to the three-dimensional (3D) incompressible Navier-Stokes (NS) and Euler systems. The global well-posedness for large amplitude smooth solutions to the Cauchy problem for 3D incompressible NS and Euler equations based on a class of variant spherical coordinates is obtained, where smooth initial data is not axi-symmetric with respect to any coordinate axis in Cartesian coordinate system. Furthermore, we establish the existence, uniqueness and exponentially decay rate in time of the global strong solution to the initial boundary value problem for 3D incompressible NS equations for a class of the smooth large initial data and a class of the special bounded domain described by variant spherical coordinates.
关键词 ：
3D incompressible Navier-Stokes and Euler equations 3D incompressible Navier-Stokes and Euler equations global well-posedness global well-posedness variant spherical coordinates variant spherical coordinates
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| GB/T 7714 | Wang, Shu , Wang, Yongxin . The Global Well-Posedness for Large Amplitude Smooth Solutions for 3D Incompressible Navier-Stokes and Euler Equations Based on a Class of Variant Spherical Coordinates [J]. | MATHEMATICS , 2020 , 8 (7) . |
| MLA | Wang, Shu et al. "The Global Well-Posedness for Large Amplitude Smooth Solutions for 3D Incompressible Navier-Stokes and Euler Equations Based on a Class of Variant Spherical Coordinates" . | MATHEMATICS 8 . 7 (2020) . |
| APA | Wang, Shu , Wang, Yongxin . The Global Well-Posedness for Large Amplitude Smooth Solutions for 3D Incompressible Navier-Stokes and Euler Equations Based on a Class of Variant Spherical Coordinates . | MATHEMATICS , 2020 , 8 (7) . |
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摘要 ：
We investigate the time-asymptotic stability of planar rarefaction wave for the 3D bipolar Vlasov Poisson Boltzmann (VPB) system, based on the micro macro decompositions introduced in [T. P. Liu and S. H. Yu, Boltzmann equation: Micro-macro decompositions and positivity of shock profiles, Comm. Math. Phys. 246 (2004) 133-179; Energy method for the Boltzmann equation, Physica D 188 (2004) 178-192] and our new observations on the underlying wave structures of the equation to overcome the difficulties due to the wave propagation along the transverse directions and its interactions with the planar rarefaction wave. Note that this is the first stability result of basic wave patterns for bipolar VPB system in three dimensions.
关键词 ：
Vlasov-Poisson-Boltzmann system Vlasov-Poisson-Boltzmann system planar rarefaction wave planar rarefaction wave stability stability
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| GB/T 7714 | Wang, Shu , Wang, Teng . Stability of planar rarefaction wave to the 3D bipolar Vlasov Poisson Boltzmann system [J]. | MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES , 2020 , 30 (1) : 23-104 . |
| MLA | Wang, Shu et al. "Stability of planar rarefaction wave to the 3D bipolar Vlasov Poisson Boltzmann system" . | MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES 30 . 1 (2020) : 23-104 . |
| APA | Wang, Shu , Wang, Teng . Stability of planar rarefaction wave to the 3D bipolar Vlasov Poisson Boltzmann system . | MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES , 2020 , 30 (1) , 23-104 . |
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摘要 ：
The purpose of this paper is to study the fluid-structure interaction (FSI) problem which is a simplified model to describe high frequency and small displacement oscillation of elastic structure in fluids. The elastic structure displacement is modeled by a fourth-order nonlinear hyperbolic square equations, the motion of fluid is modeled by the time-dependent incompressible Navier-Stokes equations. We prove the existence of at least one weak solution (global in time) to this problem by compactness method. The result both holds for two-dimensional and three-dimensional cases.
关键词 ：
global weak solutions global weak solutions Navier-Stokes equations Navier-Stokes equations compactness method compactness method FSI FSI coupled PDEs coupled PDEs
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| GB/T 7714 | Shen, Lin , Wang, Shu , Feng, Yuehong . Existence of global weak solutions for the high frequency and small displacement oscillation fluid-structure interaction systems [J]. | MATHEMATICAL METHODS IN THE APPLIED SCIENCES , 2020 , 44 (5) : 3249-3259 . |
| MLA | Shen, Lin et al. "Existence of global weak solutions for the high frequency and small displacement oscillation fluid-structure interaction systems" . | MATHEMATICAL METHODS IN THE APPLIED SCIENCES 44 . 5 (2020) : 3249-3259 . |
| APA | Shen, Lin , Wang, Shu , Feng, Yuehong . Existence of global weak solutions for the high frequency and small displacement oscillation fluid-structure interaction systems . | MATHEMATICAL METHODS IN THE APPLIED SCIENCES , 2020 , 44 (5) , 3249-3259 . |
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摘要 ：
Keller-Segel systems in two and three space dimensions with an additional cross-diffusion term in the equation for the chemical concentration are analyzed. The cross-diffusion term has a stabilizing effect and leads to the global-in-time existence of weak solutions. The limit of vanishing cross-diffusion parameter is proved rigorously in the parabolic-elliptic and parabolic-parabolic cases. When the signal production is sublinear, the existence of global-in-time weak solutions as well as the convergence of the solutions to those of the classical parabolic-elliptic Keller-Segel equations are proved. The proof is based on a reformulation of the equations eliminating the additional cross-diffusion term but making the equation for the cell density quasilinear. For superlinear signal production terms, convergence rates in the cross-diffusion parameter are proved for local-in-time smooth solutions (since finite-time blow up is possible). The proof is based on careful H-s(Omega) estimates and a variant of the Gronwall lemma. Numerical experiments in two space dimensions illustrate the theoretical results and quantify the shape of the cell aggregation bumps as a function of the cross-diffusion parameter. (C) 2019 Elsevier Ltd. All rights reserved.
关键词 ：
Vanishing cross-diffusion limit Vanishing cross-diffusion limit Higher-order estimates Higher-order estimates Numerical simulations Numerical simulations Entropy method Entropy method Keller-Segel model Keller-Segel model Asymptotic analysis Asymptotic analysis
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| GB/T 7714 | Juengel, Ansgar , Leingang, Oliver , Wang, Shu . Vanishing cross-diffusion limit in a Keller-Segel system with additional cross-diffusion [J]. | NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS , 2020 , 192 . |
| MLA | Juengel, Ansgar et al. "Vanishing cross-diffusion limit in a Keller-Segel system with additional cross-diffusion" . | NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS 192 (2020) . |
| APA | Juengel, Ansgar , Leingang, Oliver , Wang, Shu . Vanishing cross-diffusion limit in a Keller-Segel system with additional cross-diffusion . | NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS , 2020 , 192 . |
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