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学者姓名：刘继涛
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摘要 ：
In this paper, we are concerned with the initial-boundary value problem to the 2D magneto-micropolar system with zero angular viscosity in a smooth bounded domain. We prove that there exists a unique global strong solution of such a system by imposing natural boundary conditions and regularity assumptions on the initial data, without any compatibility condition.
关键词 ：
2D magneto-micropolar equations 2D magneto-micropolar equations Initial-boundary value problem Initial-boundary value problem Zero angular viscosity Zero angular viscosity
引用：
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| GB/T 7714 | Wang, Shasha , Xu, Wen-Qing , Liu, Jitao . Initial-boundary value problem for 2D magneto-micropolar equations with zero angular viscosity [J]. | ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK , 2021 , 72 (3) . |
| MLA | Wang, Shasha 等. "Initial-boundary value problem for 2D magneto-micropolar equations with zero angular viscosity" . | ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK 72 . 3 (2021) . |
| APA | Wang, Shasha , Xu, Wen-Qing , Liu, Jitao . Initial-boundary value problem for 2D magneto-micropolar equations with zero angular viscosity . | ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK , 2021 , 72 (3) . |
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摘要 ：
In this paper, we consider solutions to the incompressible axisymmetric Euler equations without swirl. The main result is to prove the global existence of weak solutions if the initial vorticity w0θ satisfies that w0θr∈L1∩Lp(R3) for some p> 1. It is not required that the initial energy is finite, that is, the initial velocity u belongs to L2(R3) here. We construct the approximate solutions by regularizing the initial data and show that the concentrations of energy do not occur in this case. The key ingredient in the proof lies in establishing the Lloc2+α(R3) estimates of velocity fields for some α> 0 , which is new to the best of our knowledge. © 2021, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
关键词 ：
Euler equations Euler equations Velocity Velocity
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| GB/T 7714 | Jiu, Quansen , Liu, Jitao , Niu, Dongjuan . Global Existence of Weak Solutions to the Incompressible Axisymmetric Euler Equations Without Swirl [J]. | Journal of Nonlinear Science , 2021 , 31 (2) . |
| MLA | Jiu, Quansen 等. "Global Existence of Weak Solutions to the Incompressible Axisymmetric Euler Equations Without Swirl" . | Journal of Nonlinear Science 31 . 2 (2021) . |
| APA | Jiu, Quansen , Liu, Jitao , Niu, Dongjuan . Global Existence of Weak Solutions to the Incompressible Axisymmetric Euler Equations Without Swirl . | Journal of Nonlinear Science , 2021 , 31 (2) . |
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摘要 ：
In this paper, we are devoted to establishing some new regularity criteria of the weak solutions to the incompressible axisymmetric Boussinesq equations, which are independent of density. To this end, we establish some new a priori estimates. To some extent, our result can be thought as a generation of that in Chae and Lee (2002) and an addition of that in Fang et al. (2018). © 2020 Elsevier Ltd
关键词 ：
Mathematical techniques Mathematical techniques
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| GB/T 7714 | Wang, Shu , Wang, Yongxin , Liu, Jitao . Regularity criteria to the incompressible axisymmetric Boussinesq equations [J]. | Applied Mathematics Letters , 2021 , 112 . |
| MLA | Wang, Shu 等. "Regularity criteria to the incompressible axisymmetric Boussinesq equations" . | Applied Mathematics Letters 112 (2021) . |
| APA | Wang, Shu , Wang, Yongxin , Liu, Jitao . Regularity criteria to the incompressible axisymmetric Boussinesq equations . | Applied Mathematics Letters , 2021 , 112 . |
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摘要 ：
In this paper, we study the asymptotic behavior of solutions to second grade fluid equations, a model for viscoelastic fluids, in an expanding domain. We prove that, the solutions converge to a solution of the incompressible Euler equations in the whole plane, as the elastic response alpha and the viscosity nu vanish, and the radius of domain becomes infinite. Meanwhile, we also establish precise convergence rates in terms of nu, alpha and the radius of the family of spatial domains. (C) 2019 Elsevier Ltd. All rights reserved.
关键词 ：
Expanding domain Expanding domain Second grade fluid equations Second grade fluid equations Vanishing alpha limits Vanishing alpha limits Vanishing viscosity limits Vanishing viscosity limits
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| GB/T 7714 | Liu, Jitao , Xu, Wen-Qing . Vanishing alpha and viscosity limits of second grade fluid equations for an expanding domain in the plane [J]. | NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS , 2019 , 49 : 355-367 . |
| MLA | Liu, Jitao 等. "Vanishing alpha and viscosity limits of second grade fluid equations for an expanding domain in the plane" . | NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS 49 (2019) : 355-367 . |
| APA | Liu, Jitao , Xu, Wen-Qing . Vanishing alpha and viscosity limits of second grade fluid equations for an expanding domain in the plane . | NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS , 2019 , 49 , 355-367 . |
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摘要 ：
It is shown in this paper that suitable weak solutions to the 6D steady incompressible Navier-Stokes and MHD equations are Holder continuous near boundary provided that either r(-3) integral(+)(Br) vertical bar u(x)vertical bar(3) dx or r(-2) integral(+)(Br) vertical bar del u(x)vertical bar(2) dx is sufficiently small, which implies that the 2D Hausdorff measure of the set of singular points near the boundary is zero. This generalizes recent interior regularity results by Dong-Strain [5]. (c) 2017 Elsevier Inc. All rights reserved.
关键词 ：
Boundary regularity Boundary regularity MHD equations MHD equations Navier-Stokes equations Navier-Stokes equations Suitable weak solutions Suitable weak solutions
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| GB/T 7714 | Liu, Jitao , Wang, Wendong . Boundary regularity criteria for the 6D steady Navier-Stokes and MHD equations [J]. | JOURNAL OF DIFFERENTIAL EQUATIONS , 2018 , 264 (3) : 2351-2376 . |
| MLA | Liu, Jitao 等. "Boundary regularity criteria for the 6D steady Navier-Stokes and MHD equations" . | JOURNAL OF DIFFERENTIAL EQUATIONS 264 . 3 (2018) : 2351-2376 . |
| APA | Liu, Jitao , Wang, Wendong . Boundary regularity criteria for the 6D steady Navier-Stokes and MHD equations . | JOURNAL OF DIFFERENTIAL EQUATIONS , 2018 , 264 (3) , 2351-2376 . |
| 导入链接 | NoteExpress RIS BibTex |
摘要 ：
This paper concerns the initial-boundary value problem for 2D micropolar equations without angular viscosity in a smooth bounded domain. It is shown that such a system admits a unique and global strong solution. The main contribution of this paper is to fully exploit the structure of this system and establish high order estimates via introducing an auxiliary field which is at the energy level of one order lower than micro-rotation.
关键词 ：
2D micropolar equations 2D micropolar equations angular viscosity angular viscosity Initial-boundary value problem Initial-boundary value problem
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| GB/T 7714 | Liu, Jitao , Wang, Shu . INITIAL-BOUNDARY VALUE PROBLEM FOR 2D MICROPOLAR EQUATIONS WITHOUT ANGULAR VISCOSITY [J]. | COMMUNICATIONS IN MATHEMATICAL SCIENCES , 2018 , 16 (8) : 2147-2165 . |
| MLA | Liu, Jitao 等. "INITIAL-BOUNDARY VALUE PROBLEM FOR 2D MICROPOLAR EQUATIONS WITHOUT ANGULAR VISCOSITY" . | COMMUNICATIONS IN MATHEMATICAL SCIENCES 16 . 8 (2018) : 2147-2165 . |
| APA | Liu, Jitao , Wang, Shu . INITIAL-BOUNDARY VALUE PROBLEM FOR 2D MICROPOLAR EQUATIONS WITHOUT ANGULAR VISCOSITY . | COMMUNICATIONS IN MATHEMATICAL SCIENCES , 2018 , 16 (8) , 2147-2165 . |
| 导入链接 | NoteExpress RIS BibTex |
摘要 ：
In this paper, we investigate the regularity criteria of axisymmetric solutions to the incompressible MHD equations, which have the form u = u(r)e(r) + u(theta)e(theta). + u(z)e(z) and b = b(theta)e(theta). Through establishing some innovative estimates, we obtain some new regularity criteria that are scaling invariant and independent of b(theta). To some extent, our work can be seen as a generation of the result by D. Chae and J. Lee [9] on the axisymmetric incompressible Navier-Stokes equations.
关键词 ：
axisymmetric axisymmetric incompressible MHD equations incompressible MHD equations Regularity criteria Regularity criteria
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| GB/T 7714 | Jiu, Quansen , Liu, Jitao . Regularity criteria to the axisymmetric incompressible Magneto-hydrodynamics equations [J]. | DYNAMICS OF PARTIAL DIFFERENTIAL EQUATIONS , 2018 , 15 (2) : 109-126 . |
| MLA | Jiu, Quansen 等. "Regularity criteria to the axisymmetric incompressible Magneto-hydrodynamics equations" . | DYNAMICS OF PARTIAL DIFFERENTIAL EQUATIONS 15 . 2 (2018) : 109-126 . |
| APA | Jiu, Quansen , Liu, Jitao . Regularity criteria to the axisymmetric incompressible Magneto-hydrodynamics equations . | DYNAMICS OF PARTIAL DIFFERENTIAL EQUATIONS , 2018 , 15 (2) , 109-126 . |
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摘要 ：
This paper focuses on the initial- and boundary-value problem for the two-dimensional micropolar equations with only angular velocity dissipation in a smooth bounded domain. The aim here is to establish the global existence and uniqueness of solutions by imposing natural boundary conditions and minimal regularity assumptions on the initial data. Besides, the global solution is shown to possess higher regularity when the initial datum is more regular. To obtain these results, we overcome two main difficulties: one due to the lack of full dissipation and one due to the boundary conditions. In addition to the global regularity problem, we also examine the large time behavior of solutions and obtain explicit decay rates.
关键词 ：
Bounded domain Bounded domain Global regularity Global regularity Micropolar equations Micropolar equations Partial dissipation Partial dissipation
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| GB/T 7714 | Jiu, Quansen , Liu, Jitao , Wu, Jiahong et al. On the initial- and boundary-value problem for 2D micropolar equations with only angular velocity dissipation [J]. | ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK , 2017 , 68 (5) . |
| MLA | Jiu, Quansen et al. "On the initial- and boundary-value problem for 2D micropolar equations with only angular velocity dissipation" . | ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK 68 . 5 (2017) . |
| APA | Jiu, Quansen , Liu, Jitao , Wu, Jiahong , Yu, Huan . On the initial- and boundary-value problem for 2D micropolar equations with only angular velocity dissipation . | ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK , 2017 , 68 (5) . |
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摘要 ：
This paper is concerned with the initial-boundary value problem to 2D magnetohydrodynamics-Boussinesq system with the temperature-dependent viscosity, thermal diffusivity and electrical conductivity. First, we establish the global weak solutions under the minimal initial assumption. Then by imposing higher regularity assumption on the initial data, we obtain the global strong solution with uniqueness. Moreover, the exponential decay rates of weak solutions and strong solution are obtained respectively. (C) 2017 Elsevier Inc. All rights reserved.
关键词 ：
Initial-boundary value problem Initial-boundary value problem MHD-Boussinesq system MHD-Boussinesq system Temperature-dependent viscosity Temperature-dependent viscosity
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| GB/T 7714 | Bian, Dongfen , Liu, Jitao . Initial-boundary value problem to 2D Boussinesq equations for MHD convection with stratification effects [J]. | JOURNAL OF DIFFERENTIAL EQUATIONS , 2017 , 263 (12) : 8074-8101 . |
| MLA | Bian, Dongfen et al. "Initial-boundary value problem to 2D Boussinesq equations for MHD convection with stratification effects" . | JOURNAL OF DIFFERENTIAL EQUATIONS 263 . 12 (2017) : 8074-8101 . |
| APA | Bian, Dongfen , Liu, Jitao . Initial-boundary value problem to 2D Boussinesq equations for MHD convection with stratification effects . | JOURNAL OF DIFFERENTIAL EQUATIONS , 2017 , 263 (12) , 8074-8101 . |
| 导入链接 | NoteExpress RIS BibTex |
摘要 ：
In this paper, we investigate the global well-posedness of three-dimensional Navier-Stokes equations with horizontal viscosity under a special symmetric structure: helical symmetry. More precisely, by a revised Ladyzhenskaya-type inequality and utilizing the behavior of helical flows, we prove the global existence and uniqueness of weak and strong solutions to the three-dimensional helical flows. Our result reveals that for the issue of global well-posedness of the viscous helical flows, the horizontal viscosity plays the important role. To some extent, our work can be seen as a generalization of the result by Mahalov et al. (Arch Ration Mech Anal 112(3): 193-222, 1990).
关键词 ：
Global well-posedness Global well-posedness Helical symmetry Helical symmetry Horizontal viscosity Horizontal viscosity Navier-Stokes equations Navier-Stokes equations
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| GB/T 7714 | Liu, Jitao , Niu, Dongjuan . Global well-posedness of three-dimensional Navier-Stokes equations with partial viscosity under helical symmetry [J]. | ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK , 2017 , 68 (3) . |
| MLA | Liu, Jitao et al. "Global well-posedness of three-dimensional Navier-Stokes equations with partial viscosity under helical symmetry" . | ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK 68 . 3 (2017) . |
| APA | Liu, Jitao , Niu, Dongjuan . Global well-posedness of three-dimensional Navier-Stokes equations with partial viscosity under helical symmetry . | ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK , 2017 , 68 (3) . |
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