Article
Mathematics, Applied
Chengfeng Sun, Fang Zhang, Hui Liu, Qingkun Xiao
Summary: The 2D magnetohydrodynamics equations with horizontal dissipation and horizontal magnetic diffusion are considered. The classical solution in H-k (k >= 2) has been obtained; due to partial dissipation and strong nonlinearity, the global well-posedness of weak solution in H(1) is still unknown. In this paper, by combining classic Galerkin's method with Brouwer's fixed point theorem, existence of time-periodic solution in H1 with small initial values is obtained.
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
(2023)
Article
Mathematics
Jiahong Wu, Yi Zhu
Summary: This paper focuses on the 2D compressible magnetohydrodynamic equations without magnetic diffusion and presents a systematic approach to establishing the global existence of smooth solutions. Stability and large-time decay rates are also obtained. The paper highlights the utilization of weak smoothing and stabilization generated by the background magnetic field and the extra regularization in the velocity field's divergence part to maximize the enhanced dissipation.
JOURNAL OF FUNCTIONAL ANALYSIS
(2022)
Article
Mathematics
Jishan Fan, Liangwei Wang, Yong Zhou
Summary: This paper proves the global existence of strong solutions to the 2D density-dependent incompressible magnetic Benard problem in a bounded domain.
BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY
(2021)
Article
Mathematics, Applied
Yanxia Niu, Yinxia Wang
Summary: This paper proves the existence of global classical large solutions for the initial value problem of two-dimensional liquid crystal flows with partial viscosity. The results are obtained by using energy estimates, anisotropic type Sobolev inequalities, and tricky interpolation techniques.
APPLIED MATHEMATICS LETTERS
(2021)
Article
Mathematics, Applied
Yaxin Du, Qian Zhang
Summary: This paper investigates a mathematical model of bioconvective patterns and a chemotaxis system coupling with Navier-Stokes equation. Global classical solutions for the incompressible four-component chemotaxis-Navier-Stokes equations in R-2 are established using Fourier localization technique and regularity criterion.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2021)
Article
Mathematics, Applied
Yina Lin, Qian Zhang, Meng Zhou
Summary: In this paper, we investigate the incompressible chemotaxis-Navier-Stokes equations with a logistic source in two-dimensional space. We firstly establish a blow-up criterion and then prove the global existence of classical solutions to the system for the Cauchy problem under certain rough conditions on the initial data.
Article
Mathematics, Applied
Hongxia Lin, Youhua Wei, Jiahong Wu
Summary: This paper investigates the stability problem of the Oldroyd-B model for incompressible non-Newtonian fluids, especially with partial dissipation. By utilizing a special wave structure and enhanced dissipation, the global stability and long-time behavior of the 2D model in a periodic domain are proven.
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
(2022)
Article
Mathematics, Applied
Matheus J. Lazarotto, Ibere L. Caldas, Yves Elskens
Summary: This study investigates diffusion transitions in a bidimensional softbilliard model under variation of control parameters. Sudden transitions between normal and ballistic regimes are found and shown to be correlated with increases in global stability area.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2022)
Article
Mathematics, Applied
Wei Li, Zhaoyang Shang, Fuquan Tang
Summary: This paper deals with the initial-boundary value problem of planar magnetohydrodynamic (MHD) equations with zero magnetic diffusivity. The global existence and uniqueness of strong solution are established when the coefficients of viscosity and heat conductivity are positive constants. The results do not impose any smallness restriction on the initial data and vacuum is allowed for the initial density.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2021)
Article
Mathematics, Applied
Jiefeng Zhao
Summary: This paper studies strong solutions to 2D generalized MHD equations with specific velocity dissipation and magnetic diffusion. It proves the existence of a unique global solution in Sobolev spaces when certain conditions are met, indicating the importance of the global regularity problem in 2D resistive MHD equations.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2022)
Article
Astronomy & Astrophysics
Rylan Jardine, Jade Powell, Bernhard Muller
Summary: This study investigates the influence of rotation and magnetic fields on the dynamics and gravitational wave emission in 2D core-collapse supernova simulations with neutrino transport. The results show that strong magnetic fields generally facilitate shock revival, while the impact of rotation on post-bounce dynamics is more diverse. Significant effects on the time-frequency structure of gravitational wave signals are only found in cases of rapid rotation or strong initial fields. Detection distances for waveforms from magnetorotational models are not notably higher during the post-bounce and explosion phase.
MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY
(2022)
Article
Mathematics, Applied
Fei Jiang, Song Jiang, Youyi Zhao
Summary: In this paper, we study the global existence for an initial-boundary value problem in a horizontally periodic domain in three dimensions. By developing a new type of two-layer energy structure, we prove that the initial-boundary value problem admits a unique and global smooth solution. The solution decays exponentially in time to some rest state.
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
(2022)
Article
Mathematics, Applied
Yajuan Zhao, Xiaoping Zhai
Summary: The construction of global small solutions to the 3D MHD system with only one damping term remains an open problem, but a positive answer is provided in T-3 under certain conditions.
APPLIED MATHEMATICS LETTERS
(2021)
Article
Mathematics, Applied
Yu Liu, Ting Zhang
Summary: This paper proves the global existence of weak solutions for a two-dimensional non-resistivity MHD system with non-monotone pressure law and density-depending viscosity using an approximate scheme and the compactness method. This result improves upon previous work by incorporating more general pressure law and viscosity.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2021)
Article
Mathematics
Ning Liu, Ping Zhang
Summary: This paper establishes the global existence and large time decay estimate of solutions to the two-dimensional MHD boundary layer equations with small initial data, which are analytical in the tangential variable. The proof is inspired by previous work but encounters additional difficulties related to the magnetic field, far field dependence on the tangential variable, and differences in Reynolds numbers. In particular, an open question regarding the large time existence of analytical solutions to the MHD boundary layer equations posed in a previous study is solved.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2021)
Article
Mathematics, Applied
Yi Zhou, Yi Zhu
ACTA MATHEMATICA SINICA-ENGLISH SERIES
(2018)
Article
Mathematics
Ronghua Pan, Yi Zhu
JOURNAL OF DIFFERENTIAL EQUATIONS
(2016)
Article
Mathematics
Yi Zhu
JOURNAL OF FUNCTIONAL ANALYSIS
(2018)
Article
Mathematics, Applied
Yi Zhu
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2020)
Article
Mathematics, Applied
Peter Constantin, Jiahong Wu, Jiefeng Zhao, Yi Zhu
Summary: The study presents a small data global well-posedness result for an incompressible Oldroyd-B model with wave-number dissipation, which is uniform in solvent Reynolds numbers and only requires fractional wave number-dependent dissipation in the added stress tensor.
JOURNAL OF EVOLUTION EQUATIONS
(2021)
Article
Mathematics
Jiahong Wu, Yi Zhu
Summary: This paper focuses on the global stability of perturbations near the steady solution of the 3D incompressible magnetohydrodynamic equations with mixed partial dissipation and magnetic diffusion. The new stability result presented here is among the very few stability conclusions currently available for ideal or partially dissipated MHD equations. As a special consequence of the techniques introduced in this paper, the small data global well-posedness for the 3D incompressible Navier-Stokes equations without vertical dissipation is obtained.
ADVANCES IN MATHEMATICS
(2021)
Article
Mathematics, Applied
Yi Zhu
Summary: This paper proves the global existence of general small solutions to compressible viscoelastic system, while removing the previous assumptions on initial state and structure, broadening the class of solutions. A new effective flux is introduced, and the wildest nonlinear term is regarded as linear term.
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
(2022)
Article
Mathematics
Xinghong Pan, Jiang Xu, Yi Zhu
Summary: We are interested in studying the characteristics of multi-dimensional compressible viscoelastic flows of Oldroyd type, which are non-Newtonian fluids exhibiting elastic behavior. In this paper, we aim to remove the structural condition and prove the global existence of strong solutions to compressible viscoelastic flows in critical spaces. By introducing a new effective flux in the absence of compatible conditions, we are able to capture the dissipation arising from the combination of density and deformation tensor. The partial dissipation in non-Newtonian compressible fluids is weaker than that in the classical Navier-Stokes equations.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2022)
Article
Mathematics
Jiahong Wu, Yi Zhu
Summary: This paper focuses on the 2D compressible magnetohydrodynamic equations without magnetic diffusion and presents a systematic approach to establishing the global existence of smooth solutions. Stability and large-time decay rates are also obtained. The paper highlights the utilization of weak smoothing and stabilization generated by the background magnetic field and the extra regularization in the velocity field's divergence part to maximize the enhanced dissipation.
JOURNAL OF FUNCTIONAL ANALYSIS
(2022)
Article
Mathematics, Applied
Ronghua Pan, Yi Zhou, Yi Zhu
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
(2018)
