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学者姓名：刘继涛
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Abstract ：
Whether the global existence and uniqueness of strong solutions to n-dimensional incompressible magnetohydrodynamic (MHD for short) equations with only kinematic viscosity or magnetic diffusion holds true or not remains an outstanding open problem. In recent years, stared from the pioneer work by Lin and Zhang (Commun Pure Appl Math 67(4):531-580, 2014), much more attention has been paid to the case when the magnetic field close to an equilibrium state (the background magnetic field for short). Specifically, when the background magnetic field satisfies the Diophantine condition (see (1.2) for details), Chen et al. (Sci China Math 41:1-10, 2022) first studied the perturbation system and established the decay estimates and asymptotic stability of its solutions in 3D periodic domain T-3, which was then improved to H(3+2 beta)r+5+(alpha+2 beta)(T-2) for 2D periodic domain T-2 and any alpha>0, beta>0 by Zhai (J Differ Equ 374:267-278, 2023). In this paper, we seek to find the optimal decay estimates and improve the space where the global stability is taking place. Through deeply exploring and effectively utilizing the structure of perturbation system, we discover a new dissipative mechanism, which enables us to establish the decay estimates in the Sobolev spaces with much lower regularity. Based on the above discovery, we greatly reduce the initial regularity requirement of aforesaid two works from H4r+7(T3) and H(3+2 beta)r+5+(alpha+2 beta)(T-2) to H(3r+3)+(T-n) for r>n-1 when n=3 and n=2 respectively. Additionally, we first present the linear stability result via the method of spectral analysis in this paper. From which, the decay estimates obtained for the nonlinear system can be seen as sharp in the sense that they are in line with those for the linearized system.
Keyword ：
35Q35 35Q35 76E25 76E25 35B35 35B35 35A01 35A01 76W05 76W05
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| GB/T 7714 | Xie, Yaowei , Jiu, Quansen , Liu, Jitao . Sharp decay estimates and asymptotic stability for incompressible MHD equations without viscosity or magnetic diffusion [J]. | CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS , 2024 , 63 (8) . |
| MLA | Xie, Yaowei 等. "Sharp decay estimates and asymptotic stability for incompressible MHD equations without viscosity or magnetic diffusion" . | CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS 63 . 8 (2024) . |
| APA | Xie, Yaowei , Jiu, Quansen , Liu, Jitao . Sharp decay estimates and asymptotic stability for incompressible MHD equations without viscosity or magnetic diffusion . | CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS , 2024 , 63 (8) . |
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In this paper, we address the Holder regularity for helicity for incompressible flows. It is shown that the helicity of incompressible Euler equations belongs to Holder spaces provided that the velocity or vorticity lies in suitable Besov spaces, which generalizes recent results in Sobolev spaces due to De Rosa (Proc Am Math Soc 148: 2969-2979, 2020). The analogue result for the incompressible fractional Navier-Stokes equations is also derived.
Keyword ：
Euler equations Euler equations Holder regularity Holder regularity Helicity Helicity Navier-Stokes equations Navier-Stokes equations
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| GB/T 7714 | Liu, Jitao , Zhao, Yunxiao . Holder Regularity of Helicity for the Incompressible Flows [J]. | JOURNAL OF MATHEMATICAL FLUID MECHANICS , 2023 , 25 (1) . |
| MLA | Liu, Jitao 等. "Holder Regularity of Helicity for the Incompressible Flows" . | JOURNAL OF MATHEMATICAL FLUID MECHANICS 25 . 1 (2023) . |
| APA | Liu, Jitao , Zhao, Yunxiao . Holder Regularity of Helicity for the Incompressible Flows . | JOURNAL OF MATHEMATICAL FLUID MECHANICS , 2023 , 25 (1) . |
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Abstract ：
In this paper, we are concerned with the Holder regularity in time of both solutions and their energy for the generalized surface quasi-geostrophic equation with the velocity v given by v = R perpendicular to Lambda gamma-1 theta. In the first part, it is shown that the regularity in time of solutions theta is Ct alpha for 0 < alpha < 1 with 0 < gamma < 1 and C alpha/gamma t for gamma - 1 < alpha < 1 with 1 < gamma < 2, as long as theta belongs to L infinity tCx alpha.In the second part, we address the Holder regularity in time of their energy and establish the corresponding criteria for the temperature in Onsager-subcritical spaces.(c) 2022 Elsevier Ltd. All rights reserved.
Keyword ：
H?lder regularity H?lder regularity Quasi-geostrophic equation Quasi-geostrophic equation Energy conservation Energy conservation
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| GB/T 7714 | Wang, Yanqing , Mei, Xue , Liu, Jitao . Holder regularity in time of solutions to the generalized surface quasi-geostrophic equation [J]. | APPLIED MATHEMATICS LETTERS , 2023 , 137 . |
| MLA | Wang, Yanqing 等. "Holder regularity in time of solutions to the generalized surface quasi-geostrophic equation" . | APPLIED MATHEMATICS LETTERS 137 (2023) . |
| APA | Wang, Yanqing , Mei, Xue , Liu, Jitao . Holder regularity in time of solutions to the generalized surface quasi-geostrophic equation . | APPLIED MATHEMATICS LETTERS , 2023 , 137 . |
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Abstract ：
We study the Cauchy problem for the 2D incompressible MHD-Boussinesq equations without thermal diffusion. We prove the global existence and uniqueness of the solutions for suitably regular initial data. To obtain large time decay properties of the solutions, we insert an artificial thermal damping term. By applying the classical Fourier splitting methods, we derive optimal large time decay rates of the solutions and their first-order derivatives.
Keyword ：
MHD-Boussinesq equations MHD-Boussinesq equations large time behavior large time behavior global well-posedness global well-posedness Fourier splitting Fourier splitting
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| GB/T 7714 | WANG, S. H. A. S. H. A. , XU, WEN-QING , LIU, J. I. T. A. O. . GLOBAL WELL-POSEDNESS AND LARGE TIME BEHAVIOR TO 2D BOUSSINESQ EQUATIONS FOR MHD CONVECTION [J]. | METHODS AND APPLICATIONS OF ANALYSIS , 2022 , 29 (1) : 31-56 . |
| MLA | WANG, S. H. A. S. H. A. 等. "GLOBAL WELL-POSEDNESS AND LARGE TIME BEHAVIOR TO 2D BOUSSINESQ EQUATIONS FOR MHD CONVECTION" . | METHODS AND APPLICATIONS OF ANALYSIS 29 . 1 (2022) : 31-56 . |
| APA | WANG, S. H. A. S. H. A. , XU, WEN-QING , LIU, J. I. T. A. O. . GLOBAL WELL-POSEDNESS AND LARGE TIME BEHAVIOR TO 2D BOUSSINESQ EQUATIONS FOR MHD CONVECTION . | METHODS AND APPLICATIONS OF ANALYSIS , 2022 , 29 (1) , 31-56 . |
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Abstract ：
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
Keyword ：
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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Abstract ：
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.
Keyword ：
2D magneto-micropolar equations 2D magneto-micropolar equations Initial-boundary value problem Initial-boundary value problem Zero angular viscosity Zero angular viscosity
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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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Abstract ：
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.
Keyword ：
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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Abstract ：
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.
Keyword ：
Expanding domain Expanding domain Vanishing viscosity limits Vanishing viscosity limits Vanishing alpha limits Vanishing alpha limits Second grade fluid equations Second grade fluid equations
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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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Abstract ：
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.
Keyword ：
MHD equations MHD equations Boundary regularity Boundary regularity Suitable weak solutions Suitable weak solutions Navier-Stokes equations Navier-Stokes equations
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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 . |
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Abstract ：
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.
Keyword ：
Regularity criteria Regularity criteria axisymmetric axisymmetric incompressible MHD equations incompressible MHD equations
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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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