Article
Mathematics, Applied
Liangliang Ma
Summary: This study focused on the asymptotic stability and large-time behavior for the 2D magnetic Benard fluid equations with mixed partial dissipation, magnetic diffusion, and thermal diffusivity. The research obtained the asymptotic stability and decay rate for the system near two steady state solutions.
APPLIED MATHEMATICS AND COMPUTATION
(2021)
Article
Mathematics, Applied
Haifeng Shang, Limin Xu
Summary: This paper focuses on the stability problem near a hydrostatic equilibrium associated with the three-dimensional Boussinesq equations with partial dissipation. The study mainly concerns the global stability, large-time behavior, and asymptotic linear stability with explicit decay rates of solutions to this system with only horizontal dissipation. These results can also be extended to the system with mixed partial dissipation.
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
(2021)
Article
Mathematics
Yajie Zhang, Jialiang Wang, Han Jiang
Summary: The paper investigates the stability of the magnetohydrodynamic equations with partial or no dissipation. The authors establish the stability near magnetic hydrostatic equilibrium for the three-dimensional magnetic Benard fluid equations with mixed partial dissipation involving viscosity, resistivity, and heat conduction. Additionally, they obtain the large-time behavior of the corresponding linearized system. The results mathematically confirm the stabilization of a background magnetic field on the three-dimensional magnetic Benard fluid.
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS
(2023)
Article
Mathematics, Applied
Ruihong Ji, Ling Tian
Summary: This paper focuses on assessing the stability of perturbations near the steady solution given by a background magnetic field in periodic domain for 3D incompressible MHD equations with mixed partial dissipation and magnetic diffusion. The new stability result presented is among few stability conclusions currently available for ideal or partially dissipated MHD equations.
Article
Mathematics, Applied
Yaqi Wan, Xiaoli Chen
Summary: This paper investigates the stability and large-time behavior of perturbations near hydrostatic equilibrium for two dimensional Boussinesq equations with horizontal dissipation and temperature diffusion. The lack of dissipation makes the stability issue more challenging compared to previous studies. The results show that the oscillation parts of the velocity and temperature only decay at a rate of (1+t)-12, which is different from previous findings.
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS
(2023)
Article
Mathematics, Applied
Liya Jiang, Youhua Wei, Kaige Yang
Summary: This paper focuses on the 3D Boussinesq equations with fractional horizontal (-Delta(h))(beta)theta and (-Delta(h))(alpha)u dissipation, and proves that if the initial data (u0,..0) in the Sobolev space H3(R3) are close enough to the hydrostatic balance state, respectively, the equations with alpha, beta in (1/2, 1] always lead to a steady solution.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Applied
Xintong Ji, Dongfen Bian
Summary: This paper establishes the nonlinear stability and large time behavior of hydrostatic equilibrium in a uniform magnetic field for the 2D Boussinesq system with magnetohydrodynamics convection on spatial domain omega=T X R-with partial dissipation. This is an important part of further work on the stability/instability of shear flow, the combination of hydrostatic equilibrium and Couette/shear flow in a uniform magnetic field with partial dissipation.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Mathematics, Applied
Yuzhu Wang, Weijia Li
Summary: This paper investigates the initial value problem for the 3D magneto-micropolar fluid equations with mixed partial viscosity and aims to establish global well-posedness of classical small solutions. The global stability of perturbations near the steady solution is proven to be given by a background magnetic field, with the proof mainly based on energy estimate and bootstrapping argument.
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
(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
Xinliang Li, Zhong Tan
Summary: In this paper, the Cauchy problem of the two-dimensional micropolar Benard problem with mixed partial viscosity is studied. The global regularity and some conditional regularity of strong solutions are obtained for the 2D micropolar Benard problem with mixed partial viscosity.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2022)
Article
Mathematics, Applied
Oussama Melkemi
Summary: The current paper focuses on the study of the 2D Benard equations with variable-viscosity. It establishes the global existence of a unique weak solution to this system without any assumptions of small initial data.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Applied
Liangliang Ma
Summary: This paper focuses on broadening the global regularity results for the two-dimensional magnetic Benard fluid equations, studying three cases and establishing global regularity for each case.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Mathematics, Applied
Xinliang Li, Zhong Tan
Summary: In this paper, the Cauchy problem of the 2D micropolar Benard system with partial viscosity is studied, and it extends the previous research on the 2D micropolar Benard system with full dissipation and angular viscosity.
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
(2022)
Article
Mechanics
Georgie Crewdson, Marcello Lappa
Summary: This article investigates the thermovibrational flow in a differentially heated cubic cavity with vibrations applied parallel to the imposed temperature gradient. Through parametric analysis, it reveals the significant influence of the intrinsic three-dimensional nature of the problem and thermal boundary conditions on the flow structures and system response.
Article
Astronomy & Astrophysics
P. Leon, E. Fuenmayor, E. Contreras
Summary: We provide a detailed analysis of a general relativistic static spherical symmetric distribution with a master polytropic equation of state to avoid singularities. The corresponding Lane-Emden equation is derived and integrated for various parameter values. The parameter space is explored to find physically reasonable solutions. Moreover, the effect of spherically symmetric perturbations on the matter variables is considered to analyze the potential occurrence of cracking within the compact distribution.
