Query：
学者姓名：王术
Refining：
Year
Type
Indexed by
Source
Complex
Co-Author
Language
Clean All
Abstract ：
In this paper, we focus on an open problem raised by Nakamura-Wada (2005) [16] & (2007) [17] on the continuous dependence issue for the Maxwell-Schr & ouml;dinger (MS) system. Motivated by the idea of Kato- Ponce for Navier-Stokes flow, here we combine approximate argument and small parameter analysis to prove the continuous dependence for a less regular strong solution. In addition, driven by the open problem on the uniqueness of energy solutions by Guo-Nakamitsu-Strauss (1995) [9], we also present a result analogous to weak-strong uniqueness through modified energy estimates and small parameter analysis. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.
Keyword ：
Uniqueness Uniqueness Continuous dependence Continuous dependence Energy multiplier Energy multiplier Moderate solution Moderate solution
Cite：
Copy from the list or Export to your reference management。
| GB/T 7714 | Shi, Qihong , Wang, Shu , Yang, Jianwei . Small parameters analysis applied to two potential issues for Maxwell-Schrödinger system [J]. | JOURNAL OF DIFFERENTIAL EQUATIONS , 2025 , 424 : 637-659 . |
| MLA | Shi, Qihong 等. "Small parameters analysis applied to two potential issues for Maxwell-Schrödinger system" . | JOURNAL OF DIFFERENTIAL EQUATIONS 424 (2025) : 637-659 . |
| APA | Shi, Qihong , Wang, Shu , Yang, Jianwei . Small parameters analysis applied to two potential issues for Maxwell-Schrödinger system . | JOURNAL OF DIFFERENTIAL EQUATIONS , 2025 , 424 , 637-659 . |
| Export to | NoteExpress RIS BibTex |
Abstract ：
This paper investigates the large-time asymptotic behavior of contact waves in 1-D compressible Navier-Stokes equations. We derive the optimal decay rate for generic initial perturbations, meaning the perturbation's integral does not need to be zero. It is well-known that generic perturbations in Navier-Stokes equations generate diffusion waves, implying that the optimal decay rate for contact waves in the L infinity-norm is (1 + t) -1 / 2 . However, the presence of diffusion waves introduces error terms, leading to energy growth in the anti-derivatives of the perturbations. Furthermore, studying contact waves depends on certain structural conditions, which hold for the original system but not for its derivative systems. This makes it challenging to obtain accurate estimates for the energy of the derivatives. In this paper, we refine the estimates for both anti-derivatives and the original perturbations. We then introduce an innovative transformation to ensure that the structural conditions continue to hold for the system of derivatives. With this approach, we achieve better estimates for the derivatives, leading to the optimal decay rates. This result improves upon the wellknown findings of Huang et al. (2008), and the method has the potential for application in more general systems.
Keyword ：
Optimal decay rate Optimal decay rate Compressible Navier-Stokes equations Compressible Navier-Stokes equations Contact wave Contact wave
Cite：
Copy from the list or Export to your reference management。
| GB/T 7714 | Liu, Lingjun , Qiu, Guiqin , Wang, Shu et al. Optimal decay rate to the contact discontinuity for Navier-Stokes equations under generic perturbations [J]. | APPLIED MATHEMATICS LETTERS , 2025 , 163 . |
| MLA | Liu, Lingjun et al. "Optimal decay rate to the contact discontinuity for Navier-Stokes equations under generic perturbations" . | APPLIED MATHEMATICS LETTERS 163 (2025) . |
| APA | Liu, Lingjun , Qiu, Guiqin , Wang, Shu , Xu, Lingda . Optimal decay rate to the contact discontinuity for Navier-Stokes equations under generic perturbations . | APPLIED MATHEMATICS LETTERS , 2025 , 163 . |
| Export to | NoteExpress RIS BibTex |
Abstract ：
This paper is concerned with the Cauchy problem for a 3D fluid-particle interaction model in the so-called flowing regime in & Ropf;3. Under the smallness assumption on both the external potential and the initial perturbation of the stationary solution in some Sobolev spaces, the existence and uniqueness of global smooth solutions in H3 of the system are established by using the careful energy method.
Keyword ：
global existence global existence flowing regime flowing regime fluid-particle fluid-particle
Cite：
Copy from the list or Export to your reference management。
| GB/T 7714 | Zheng, Lin , Wang, Shu . The global existence and uniqueness of smooth solutions to a fluid-particle interaction model in the flowing regime [J]. | ACTA MATHEMATICA SCIENTIA , 2024 , 44 (5) : 1877-1885 . |
| MLA | Zheng, Lin et al. "The global existence and uniqueness of smooth solutions to a fluid-particle interaction model in the flowing regime" . | ACTA MATHEMATICA SCIENTIA 44 . 5 (2024) : 1877-1885 . |
| APA | Zheng, Lin , Wang, Shu . The global existence and uniqueness of smooth solutions to a fluid-particle interaction model in the flowing regime . | ACTA MATHEMATICA SCIENTIA , 2024 , 44 (5) , 1877-1885 . |
| Export to | NoteExpress RIS BibTex |
Abstract ：
In this paper, we construct a family of global-in-time solutions of the 3-D full compressible Navier-Stokes (N-S) equations with temperature-dependent transport coefficients (including viscosity and heat-conductivity), and show that at arbitrary times and arbitrary strength this family of solutions converges to planar rarefaction waves connected to the vacuum as the viscosity vanishes in the sense of L infinity(R3)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L<^>\infty ({\mathbb {R}}<^>3)$$\end{document}. We consider the Cauchy problem in R3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {R}}<^>3$$\end{document} with perturbations of the infinite global norm, particularly, periodic perturbations. To deal with the infinite oscillation, we construct a suitable ansatz carrying this periodic oscillation such that the difference between the solution and the ansatz belongs to some Sobolev space and thus the energy method is feasible. The novelty of this paper is that the viscosity and heat-conductivity are temperature-dependent and degeneracies caused by vacuum. Thus the a priori assumptions and two Gagliardo-Nirenberg type inequalities are essentially used. Next, more careful energy estimates are carried out in this paper, by studying the zero and non-zero modes of the solutions, we obtain not only the convergence rate concerning the viscosity and heat conductivity coefficients but also the exponential time decay rate for the non-zero mode.
Keyword ：
35Q31 35Q31 35Q30 35Q30 76N06 76N06 35Q35 35Q35 76N10 76N10
Cite：
Copy from the list or Export to your reference management。
| GB/T 7714 | Hou, Meichen , Liu, Lingjun , Wang, Shu et al. Vanishing viscosity limit to the planar rarefaction wave with vacuum for 3-D full compressible Navier-Stokes equations with temperature-dependent transport coefficients [J]. | MATHEMATISCHE ANNALEN , 2024 , 390 (3) : 3513-3566 . |
| MLA | Hou, Meichen et al. "Vanishing viscosity limit to the planar rarefaction wave with vacuum for 3-D full compressible Navier-Stokes equations with temperature-dependent transport coefficients" . | MATHEMATISCHE ANNALEN 390 . 3 (2024) : 3513-3566 . |
| APA | Hou, Meichen , Liu, Lingjun , Wang, Shu , Xu, Lingda . Vanishing viscosity limit to the planar rarefaction wave with vacuum for 3-D full compressible Navier-Stokes equations with temperature-dependent transport coefficients . | MATHEMATISCHE ANNALEN , 2024 , 390 (3) , 3513-3566 . |
| Export to | NoteExpress RIS BibTex |
Abstract ：
In this article, we consider the blowup phenomenon of smooth solutions to the isentropic compressible quantum hydrodynamic model (QHD) with the initial density of compact support in arbitrary space dimensions.
Keyword ：
compressible quantum hydrodynamic model compressible quantum hydrodynamic model smooth solutions smooth solutions blowup blowup
Cite：
Copy from the list or Export to your reference management。
| GB/T 7714 | Zhang, Jie , Wang, Shu , Geng, Fan . Blowup of smooth solutions to the isentropic compressible quantum hydrodynamic model [J]. | MATHEMATICAL METHODS IN THE APPLIED SCIENCES , 2022 , 45 (17) : 10917-10924 . |
| MLA | Zhang, Jie et al. "Blowup of smooth solutions to the isentropic compressible quantum hydrodynamic model" . | MATHEMATICAL METHODS IN THE APPLIED SCIENCES 45 . 17 (2022) : 10917-10924 . |
| APA | Zhang, Jie , Wang, Shu , Geng, Fan . Blowup of smooth solutions to the isentropic compressible quantum hydrodynamic model . | MATHEMATICAL METHODS IN THE APPLIED SCIENCES , 2022 , 45 (17) , 10917-10924 . |
| Export to | NoteExpress RIS BibTex |
Abstract ：
We are concerned with the time-asymptotic stability of planar rarefaction wave to a non-conservative two-phase flow system described by two-dimentional compressible Euler and Navier-Stokes equations through drag force. In this paper, we show the planar rarefaction wave to a non-conservative compressible two-phase model is asymptotically stable under small initial perturbation in H-3. The main difficulties overcome in this paper come from the non-viscosity of one fluid and the interaction between two fluids caused by drag force. The stability result is proved by the energy method.
Keyword ：
planar rarefaction wave planar rarefaction wave asymptotic stability asymptotic stability energy method energy method Two-phase flow Two-phase flow
Cite：
Copy from the list or Export to your reference management。
| GB/T 7714 | Wang, Shu , Zhao, Yixuan . ASYMPTOTIC STABILITY OF PLANAR RAREFACTION WAVE TO A MULTI-DIMENSIONAL TWO-PHASE FLOW [J]. | DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B , 2022 , 28 (1) : 623-647 . |
| MLA | Wang, Shu et al. "ASYMPTOTIC STABILITY OF PLANAR RAREFACTION WAVE TO A MULTI-DIMENSIONAL TWO-PHASE FLOW" . | DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B 28 . 1 (2022) : 623-647 . |
| APA | Wang, Shu , Zhao, Yixuan . ASYMPTOTIC STABILITY OF PLANAR RAREFACTION WAVE TO A MULTI-DIMENSIONAL TWO-PHASE FLOW . | DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B , 2022 , 28 (1) , 623-647 . |
| Export to | NoteExpress RIS BibTex |
Abstract ：
An impulsive integrated pest management system with diffusion is investigated within this paper. The conditions for pest eradication of the impulsive system without natural enemies are established based on the Krein-Rutman theorem and the comparison principle for parabolic equations. Integrated pest management can be achieved at an exponential rate, when the principal eigenvalues of the auxiliary system is large enough. Numerical simulations are presented to demonstrate the theoretical results. A discussion is given at the end.
Keyword ：
Integrated pest management Integrated pest management pest control pest control eigenvalue problem eigenvalue problem diffusion diffusion
Cite：
Copy from the list or Export to your reference management。
| GB/T 7714 | Hongling, Zhou , Lin, Shen , Shu, Wang . Integrated Pest Management System with Impulsive Control of Spatial Heterogeneity [J]. | JOURNAL OF PARTIAL DIFFERENTIAL EQUATIONS , 2022 , 35 (1) : 31-48 . |
| MLA | Hongling, Zhou et al. "Integrated Pest Management System with Impulsive Control of Spatial Heterogeneity" . | JOURNAL OF PARTIAL DIFFERENTIAL EQUATIONS 35 . 1 (2022) : 31-48 . |
| APA | Hongling, Zhou , Lin, Shen , Shu, Wang . Integrated Pest Management System with Impulsive Control of Spatial Heterogeneity . | JOURNAL OF PARTIAL DIFFERENTIAL EQUATIONS , 2022 , 35 (1) , 31-48 . |
| Export to | NoteExpress RIS BibTex |
Abstract ：
In this paper, we are concerned with the global existence of generalized solutions of one-dimensional time-dependent Thomas-Fermi equations of quantum theory of atoms. We will use the vanishing artificial viscosity method. First, a special flux approximate is introduced to ensure the uniform boundedness of the electric field E-epsilon,E-sigma and the a priori L-infinity estimate, 0 < 2 sigma <= n(epsilon,sigma) <= M(t), (sic)(u(epsilon,sigma)(sic) <= M(t), where M(t) could tend to infinity as the time t tends to infinity, on the viscosity-flux approximate solutions (n(epsilon,sigma), u(epsilon,sigma)). Second, a technique, to apply the maximum principle to the combination of the Riemann invariants and (sic)(-infinity)(x) n(epsilon,sigma) (y, t)- 2 sigma dy, deduces the uniform L-infinity estimate, 0 < 2 sigma <= n(epsilon,sigma) < M, (sic)u(epsilon,sigma & nbsp;)(sic) <= M, independent of the time t and epsilon, sigma. Finally, the compensated compactness theory is applied to prove the almost everywhere convergence of (n(epsilon,sigma), u(epsilon,sigma)) as epsilon and (sigma) tend to zero. The limit (n(x, t), u(x, t)) is a global generalized solution. (c) 2022 Elsevier Ltd. All rights reserved.
Keyword ：
Viscosity method Viscosity method Maximum principle Maximum principle equations equations Global generalized solution Global generalized solution Compensated compactness method Compensated compactness method Time-dependent Thomas-Fermi Time-dependent Thomas-Fermi
Cite：
Copy from the list or Export to your reference management。
| GB/T 7714 | Wang, Shu , Ren, Yabo . The global existence of generalized solutions to the time-dependent Thomas-Fermi equations [J]. | NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS , 2022 , 219 . |
| MLA | Wang, Shu et al. "The global existence of generalized solutions to the time-dependent Thomas-Fermi equations" . | NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS 219 (2022) . |
| APA | Wang, Shu , Ren, Yabo . The global existence of generalized solutions to the time-dependent Thomas-Fermi equations . | NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS , 2022 , 219 . |
| Export to | NoteExpress RIS BibTex |
Abstract ：
In this paper, we study the asymptotic behavior of the non-autonomous stochastic 3D Brinkman-Forchheimer equations on unbounded domains. We first define a continuous non-autonomous cocycle for the stochastic equations, and then prove that the existence of tempered random attractors by Ball's idea of energy equations. Furthermore, we obtain that the tempered random attractors are periodic when the deterministic non-autonomous external term is periodic in time.
Keyword ：
non-autonomous non-autonomous random attractors random attractors unbounded domains unbounded domains Stochastic Brinkman-Forchheimer equations Stochastic Brinkman-Forchheimer equations
Cite：
Copy from the list or Export to your reference management。
| GB/T 7714 | Wang, Shu , Si, Mengmeng , Yang, Rong . RANDOM ATTRACTORS FOR NON-AUTONOMOUS STOCHASTIC BRINKMAN-FORCHHEIMER EQUATIONS ON UNBOUNDED DOMAINS [J]. | COMMUNICATIONS ON PURE AND APPLIED ANALYSIS , 2022 , 21 (5) : 1621-1636 . |
| MLA | Wang, Shu et al. "RANDOM ATTRACTORS FOR NON-AUTONOMOUS STOCHASTIC BRINKMAN-FORCHHEIMER EQUATIONS ON UNBOUNDED DOMAINS" . | COMMUNICATIONS ON PURE AND APPLIED ANALYSIS 21 . 5 (2022) : 1621-1636 . |
| APA | Wang, Shu , Si, Mengmeng , Yang, Rong . RANDOM ATTRACTORS FOR NON-AUTONOMOUS STOCHASTIC BRINKMAN-FORCHHEIMER EQUATIONS ON UNBOUNDED DOMAINS . | COMMUNICATIONS ON PURE AND APPLIED ANALYSIS , 2022 , 21 (5) , 1621-1636 . |
| Export to | NoteExpress RIS BibTex |
Abstract ：
The quasineutral limit and the mixed layer problem of the bipolar drift-diffusion model for semiconductors with different mobilities are studied in one dimensional space in this paper. For the general smooth doping profile, the general initial data and the different mobilities of electrons and holes, the quasineutral limit is proven by the matched asymptotic expansion method of singular perturbation problem and the energy method.
Keyword ：
quasineutral limit quasineutral limit mobility mobility Drift-diffusion model Drift-diffusion model mixed layer mixed layer
Cite：
Copy from the list or Export to your reference management。
| GB/T 7714 | Liu, Chundi , Wang, Shu . Mixed Layer Problem and Quasineutral Limit of the Bipolar Drift-Diffusion Model with Different Mobilities [J]. | RESULTS IN MATHEMATICS , 2022 , 77 (5) . |
| MLA | Liu, Chundi et al. "Mixed Layer Problem and Quasineutral Limit of the Bipolar Drift-Diffusion Model with Different Mobilities" . | RESULTS IN MATHEMATICS 77 . 5 (2022) . |
| APA | Liu, Chundi , Wang, Shu . Mixed Layer Problem and Quasineutral Limit of the Bipolar Drift-Diffusion Model with Different Mobilities . | RESULTS IN MATHEMATICS , 2022 , 77 (5) . |
| Export to | NoteExpress RIS BibTex |
Export
| Results： |
Selected to |
| Format： |
