Article
Mathematics, Applied
Jingbo Wu, Qingqing Wang, Qiueyue Zhang, Bo-Qing Dong
Summary: This paper deals with the global smooth solution of the 3D generalized magneto-micropolar equations. By making new observations on the nonlinear structure of the magneto-micropolar equations, it is shown that the system has a unique global smooth solution when the velocity dissipation is logarithmically hyperdissipative and the magnetic diffusion is fractional Laplacian.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics
Hongxia Lin, Sen Liu, Heng Zhang, Ru Bai
Summary: This paper investigates the global regularity of 2D incompressible anisotropic magneto-micropolar fluid equations with partial viscosity. Compared to Ma [22], this paper studies 12 cases in [22] and some other new cases, and provides new regular conditions, improving the results in [22] in terms of weaker regular criteria.
ACTA MATHEMATICA SCIENTIA
(2023)
Article
Mathematics
Yuze Deng, Ling Zhou
Summary: The study focuses on the Cauchy problem of three-dimensional incompressible magnetomicropolar fluid equations, with a nonlinear damping term in the momentum equations. By analyzing cancelation properties of the system, the researchers demonstrate the existence of a unique global strong solution for beta values greater than or equal to 4. This work extends previous results in the field.
BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY
(2021)
Article
Mathematics, Applied
Jishan Fan, Xin Zhong
Summary: By applying delicate energy estimates, we demonstrate regularity criteria for strong solutions to the 3D nonhomogeneous magneto-micropolar fluid equations with vacuum.
APPLIED MATHEMATICS LETTERS
(2023)
Article
Mathematics, Applied
Fan Wu
Summary: The study presents a sufficient condition to ensure the smoothness of solutions to 3D magneto-micropolar fluid equations by refining and extending previous results in incompressible Navier-Stokes equations, micropolar fluid equations, and MHD equations.
JOURNAL OF EVOLUTION EQUATIONS
(2021)
Article
Mathematics, Applied
Lihua Deng, Haifeng Shang
Summary: This paper investigates the global well-posedness problem for the n-dimensional magneto-micropolar equations with hyperdissipation. By exploiting the special structure of the system and energy methods, the study establishes the global existence and uniqueness of solutions, improving known global regularity results in the field.
APPLIED MATHEMATICS LETTERS
(2021)
Article
Mathematics, Applied
Hong Chen, Yimin Sun, Xin Zhong
Summary: This paper deals with the three-dimensional Cauchy problem of compressible isentropic magneto-micropolar fluid equations with initial density containing vacuum states. By using energy method and the structural characteristics of the model, the global existence of classical solutions is shown under the condition that [(γ-1)(1/a) + ν - (1/4)]E0 is suitably small, where γ, ν, and E0 represent the adiabatic exponent, resistivity coefficient, and initial energy, respectively. This result extends the work of Wei-Guo-Li (J. Differential Equations, 263: 2457-2480, 2017), where the global existence of smooth solutions was established under the condition that the initial data are small perturbations of some given constant state.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
(2023)
Article
Mathematics, Applied
Qingmei Xu, Xin Zhong
Summary: This paper establishes the local well-posedness of the barotropic compressible magneto-micropolar fluid equations with initial density containing vacuum states. It proves the local existence and uniqueness of strong solutions in bounded domains or the whole space R-3, without the need for compatibility condition on the initial data.
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
(2022)
Article
Mathematics
Hui Zhang
Summary: This paper investigates the blow-up criteria of strong solutions to the 3-dimensional incompressible micropolar fluid equations with partial viscosities, providing two criteria for the local-in-time strong solution. The proof relies on energy estimates and harmonic analysis methods.
ROCKY MOUNTAIN JOURNAL OF MATHEMATICS
(2021)
Article
Mathematics, Applied
Huanyuan Li
Summary: This paper focuses on the Cauchy problem of the three-dimensional nonhomogeneous incompressible micropolar fluid equations in the whole space. A weak Serrin-type blowup criterion for the strong solutions is established. It is proven that the strong solution exists globally for the Cauchy problem of the three-dimensional nonhomogeneous micropolar equations if the velocity satisfies the weak Serrin's condition, irrespective of the micro-rotational velocity. As an immediate application, it is further shown that the Cauchy problem of micropolar fluid equations has a unique global strong solution when the kinematic viscosity is sufficiently large, or the upper bound of initial density or initial kinetic energy is small enough.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2023)
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, Applied
Hailong Ye, Yiqiu Mao, Yan Jia
Summary: This study focuses on the optimal time rates of weak solutions for the 2D magneto-micropolar equations with micro-rotational dissipation and magnetic diffusion. The obtained optimal time decay rates of weak solutions are ||del u(t)|(|L)2+||del w(t)||(L2) <= C(1+t)(-2) and ||del b(t)||(Lp) <= C(1+t)(-1/2-(1-1/p)) with p is an element of [2, infinity).
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Mathematics, Applied
Ru Bai, Tiantian Chen, Sen Liu
Summary: This paper analyzes the stability of the two-dimensional incompressible anisotropic magneto-micropolar fluid equations near a background magnetic field. It establishes stability for both linear and nonlinear systems, providing explicit decay rates for the linear system and assessing nonlinear stability through a priori estimates and bootstrapping arguments. Results show that perturbations near a background magnetic field are globally stable in the Sobolev space H-2(R-2).
Article
Mathematics, Applied
Xuewen Wang, Keke Lei, Chenggang Liu, Pigong Han
Summary: This paper studies the existence and decay estimates of weak solutions to the 3D nonhomogeneous magneto-micropolar equations. Global existence of weak solutions is obtained, followed by the derivation of L2 and H1 decay rates for the weak solutions (u,w,b). Additionally, the H2 decay rate of the magnetic field b is obtained.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Applied
Yan Jia, Qianqian Xie, Bo-Qing Dong
Summary: This paper investigates the global regularity of 3D magneto-micropolar equations. Based on new observation of the nonlinear structure and sharp a priori estimates, the global existence of smooth solutions for the system with minimal dissipation is examined.
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
(2022)
Article
Mathematics, Applied
Manh Tuan Hoang, Matthias Ehrhardt
Summary: In this paper, a simple approach for solving stiff problems is proposed. Through nonlinear approximation and rigorous mathematical analysis, a class of explicit second-order one-step methods with L-stability and second-order convergence are constructed. The proposed methods generalize and improve existing nonstandard explicit integration schemes, and can be extended to higher-order explicit one-step methods.
APPLIED MATHEMATICS LETTERS
(2024)
Article
Mathematics, Applied
Jian Liu, Zengqin Zhao
Summary: In this article, we investigate p(x)-biharmonic equations involving Leray-Lions type operators and Hardy potentials. Some new theorems regarding the existence of generalized solutions are reestablished for such equations when the Leray-Lions type operator and the nonlinearity satisfy suitable hypotheses in variable exponent Lebesgue spaces.
APPLIED MATHEMATICS LETTERS
(2024)
Article
Mathematics, Applied
Chengcheng Cheng, Rong Yuan
Summary: This paper investigates the spreading dynamics of a nonlocal diffusion KPP model with free boundaries in time almost periodic media. By applying the novel positive time almost periodic function and satisfying the threshold condition for the kernel function, the unique asymptotic spreading speed of the free boundary problem is accurately expressed.
APPLIED MATHEMATICS LETTERS
(2024)
Article
Mathematics, Applied
Xia Wang, Xin Meng, Libin Rong
Summary: In this study, a multiscale model incorporating the modes of infection and types of immune responses of HCV is developed. The basic and immune reproduction numbers are derived and five equilibria are identified. The global asymptotic stability of the equilibria is established using Lyapunov functions, highlighting the significant impact of the reproduction numbers on the overall stability of the model.
APPLIED MATHEMATICS LETTERS
(2024)
Article
Mathematics, Applied
Junpu Li, Lan Zhang, Shouyu Cai, Na Li
Summary: This research proposes a regularized singular boundary method for quickly calculating the singularity of the special Green's function at origin. By utilizing the special Green's function and the origin intensity factor technique, an explicit intensity factor suitable for three-dimensional ocean dynamics is derived. The method does not involve singular integrals, resulting in improved computational efficiency and accuracy.
APPLIED MATHEMATICS LETTERS
(2024)
Article
Mathematics, Applied
Ying Dong, Shuai Zhang, Yichen Zhang
Summary: This paper investigates a 2D chemotaxis-consumption system with rotation and no-flux-Dirichlet boundary conditions. It proves that under certain conditions on the rotation angle, the corresponding initial-boundary value problem has a classical solution that blows up at a finite time.
APPLIED MATHEMATICS LETTERS
(2024)
Article
Mathematics, Applied
Shuhan Yao, Qi Hong, Yuezheng Gong
Summary: In this article, an extended quadratic auxiliary variable method is introduced for a droplet liquid film model. The method shows good numerical solvability and accuracy.
APPLIED MATHEMATICS LETTERS
(2024)
Article
Mathematics, Applied
Tong Wang, Binxiang Dai
Summary: This paper investigates the spreading speed and traveling wave of an impulsive reaction-diffusion model with non-monotone birth function and age structure, which models the evolution of annually synchronized emergence of adult population with maturation. The result extends the work recently established in Bai, Lou, and Zhao (J. Nonlinear Sci. 2022). Numerical simulations are conducted to illustrate the findings.
APPLIED MATHEMATICS LETTERS
(2024)
Article
Mathematics, Applied
Dinghao Zhu, Xiaodong Zhu
Summary: This paper constructs the soliton solutions of the KdV equation with non-zero background using the Riemann-Hilbert approach. The irregular Riemann-Hilbert problem is first constructed by direct and inverse scattering transform, and then regularized by introducing a novel transformation. The residue theorem is applied to derive the multi-soliton solutions at the simple poles of the Riemann-Hilbert problem. In particular, the interaction dynamics of the two-soliton solution are illustrated by considering their evolutions at different time.
APPLIED MATHEMATICS LETTERS
(2024)
Article
Mathematics, Applied
Danhua He, Liguang Xu
Summary: This paper investigates the stability of conformable fractional delay differential systems with impulses. By establishing a conformable fractional Halanay inequality, the paper provides sufficient criteria for the conformable exponential stability of the systems.
APPLIED MATHEMATICS LETTERS
(2024)
Article
Mathematics, Applied
Fei Sun, Xiaoli Li, Hongxing Rui
Summary: This paper presents a high-order numerical scheme for solving the compressible wormhole propagation problem. The scheme utilizes the fourth-order implicit Runge-Kutta method and the block-centered finite difference method, along with high-order interpolation technique and cut-off approach to achieve high-order and bound-preserving.
APPLIED MATHEMATICS LETTERS
(2024)
Article
Mathematics, Applied
Zhijie Du, Huoyuan Duan
Summary: This study analyzes a direct discretization method for computing the eigenvalues of the Maxwell eigenproblem. It utilizes a specific finite element space and the classical variational formulation, and proves the convergence of the obtained finite element solutions.
APPLIED MATHEMATICS LETTERS
(2024)
Article
Mathematics, Applied
Hongliang Li, Pingbing Ming
Summary: This paper proposes an asymptotic-preserving finite element method for solving a fourth order singular perturbation problem, which preserves the asymptotic transition of the underlying partial differential equation. The NZT element is analyzed as a representative, and a linear convergence rate is proved for the solution with sharp boundary layer. Numerical examples in two and three dimensions are consistent with the theoretical prediction.
APPLIED MATHEMATICS LETTERS
(2024)
Article
Mathematics, Applied
Shuyang Xue, Yongli Song
Summary: This paper investigates the spatiotemporal dynamics of the memory-based diffusion equation driven by memory delay and nonlocal interaction. The nonlocal interaction, characterized by the given Green function, leads to inhomogeneous steady states with any modes. The joint effect of nonlocal interaction and memory delay can result in spatially inhomogeneous Hopf bifurcation and Turing-Hopf bifurcation.
APPLIED MATHEMATICS LETTERS
(2024)
Article
Mathematics, Applied
Baoquan Zhou, Ningzhong Shi
Summary: This paper develops a stochastic SEIS epidemic model perturbed by Black-Karasinski process and investigates the impact of random fluctuations on disease outbreak. The results show that random fluctuations facilitate disease outbreak, and a sufficient condition for disease persistence is established.
APPLIED MATHEMATICS LETTERS
(2024)