Article
Mathematics, Applied
Zhengguang Guo, Dongfu Tong, Weiming Wang
Summary: This paper establishes a new regularity criterion for the 3D incompressible MHD equations by considering different weights in spatial variables. It shows that if certain space-time integrable conditions are satisfied by the partial derivatives and the magnetic field, then a weak solution is actually regular, providing new insights into the regularity theory of weak solutions.
APPLIED MATHEMATICS LETTERS
(2021)
Article
Mathematics, Applied
Shujuan Wang, Miaoqing Tian, Rijian Su
Summary: A blow-up criterion for the strong solutions of the nonhomogeneous incompressible MHD system with vacuum is established, showing the dominant role of the velocity field in the system.
JOURNAL OF FUNCTION SPACES
(2022)
Article
Mathematics, Applied
Wenjuan Wang, Zhuan Ye
Summary: The aim of this paper is to establish a regularity criterion for the three-dimensional incompressible Hall-magnetohydrodynamic equations involving only the vorticity. Our result complements and improves some existing results.
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
(2023)
Article
Mathematics
Zhuan Ye
Summary: This paper investigates the well-posedness results of the three-dimensional incompressible Hall magnetohydrodynamic equations with fractional dissipation. The authors provide a direct proof of the local well-posedness of smooth solutions for the Hall-magnetohydrodynamic equations with the diffusive term for the magnetic field consisting of the fractional Laplacian with its power bigger than or equal to one half. Furthermore, they derive the small data global well-posedness results, and obtain the optimal decay rate when the fractional powers are further restricted to a certain range.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2022)
Article
Mathematics, Applied
I Kukavica, W. S. Ozanski
Summary: The study shows the existence of an appropriate weak solution to the incompressible Navier-Stokes equations under certain conditions, and provides a detailed description of the properties of the solution. The spatial form of the study exhibits a logarithmic-type variation over time and has a critical influence on the scaling properties of the equations.
APPLIED MATHEMATICS LETTERS
(2021)
Article
Mathematics, Applied
Ines Ben Omrane, Sadek Gala, Maria Alessandra Ragusa
Summary: This paper establishes an improved regularity criterion for weak solutions of 3D incompressible MHD equations, showing that weak solutions are regular under certain conditions. This improvement builds upon previous works in the field.
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
(2021)
Article
Mathematics, Applied
Zhengguang Guo, Shunhang Zhang
Summary: In this paper, a new regularity criterion for weak solutions to the 3D incompressible MHD equations is established involving products of partial derivatives and conditions in the Lp space. It is proven that the solution is smooth over a certain time interval by satisfying certain criteria in the Lp space.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Mathematics, Applied
Jishan Fan, Yong Zhou
Summary: This paper demonstrates uniform regularity for a density-dependent incompressible Hall-MHD system.
APPLIED MATHEMATICS LETTERS
(2022)
Article
Mathematics, Applied
Zhiyong Si, Mingyi Wang, Yunxia Wang
Summary: In this paper, a linearized projection scheme for non-stationary incompressible coupled MHD with heat equations is introduced, which effectively handles the buoyancy caused by temperature differences and preserves Gauss's law naturally. The stability and error estimates of velocity, pressure, magnetic field, and temperature are verified, and the numerical results confirm the optimal convergence order and the preservation of Gauss's law.
APPLIED MATHEMATICS AND COMPUTATION
(2022)
Article
Mathematics, Applied
Shu Wang, Yongxin Wang, Jitao Liu
Summary: This paper focuses on establishing new regularity criteria for weak solutions to the incompressible axisymmetric Boussinesq equations independent of density, by introducing new a priori estimates. The results can be seen as an extension of previous work by Chae and Lee (2002) and a complement to the study by Fang et al. (2018).
APPLIED MATHEMATICS LETTERS
(2021)
Article
Mathematics, Applied
Jiri Neustupa, Minsuk Yang
Summary: This paper investigates the pressure and regularity of weak solutions to the MHD equations, showing that pressure can always be assigned to a weak solution under certain conditions. It also provides integrability conditions and regularity criteria for the pressure function, as well as remarks on similar results for different types of boundary conditions.
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
(2021)
Article
Mathematics, Applied
Hi Jun Choe, Jiri Neustupa, Minsuk Yang
Summary: This paper presents new regularity criteria based on the negative part of the pressure or the positive part of the extended Bernoulli pressure. The criteria extend the previously known results and the extension is enabled by the use of an appropriate Orlicz norm.
APPLIED MATHEMATICS LETTERS
(2022)
Article
Mathematics, Applied
Pan Liu
Summary: The paper studies the Liouville-type problem for three-dimensional stationary incompressible inhomogeneous MHD and Hall-MHD equations without any integrability condition for (del u, del B). Specifically, it demonstrates that the velocity field u and the magnetic field B, which satisfy suitable growth conditions for the mean oscillations of potential functions at infinity, are zero when the density rho is essentially bounded.
BANACH JOURNAL OF MATHEMATICAL ANALYSIS
(2023)
Article
Mathematics, Applied
Jiri Neustupa, Minsuk Yang
Summary: The article assumes that Omega is either the whole space R-3, a half-space, or a smooth bounded or exterior domain in R-3; T > 0, and (u, b, p) is a suitable weak solution of the MHD equations in Omega x (0, T). The study shows that if the sum of the L-3-norms of u and b over an arbitrarily small ball B-rho(x(0)) is finite as t approaches t(0)-, then (x(0), t(0)) is a regular point of the solution (u, b, p).
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2021)
Article
Mathematics, Applied
TianLi LI, Wen Wang, Lei Liu
Summary: The regularity criteria of the weak solutions to the 3D incompressible MHD equations are discussed, highlighting the importance of the scalar pressure field. It is shown that the weak solution is regular over a specific time interval in the Besov spaces.
JOURNAL OF FUNCTION SPACES
(2021)
Article
Mathematics, Applied
Zujin Zhang
APPLIED MATHEMATICS LETTERS
(2019)
Article
Mathematics, Applied
Zujin Zhang, Weihua Wang, Xian Yang
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2019)
Article
Mathematics, Applied
Tong Tang, Zujin Zhang
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
(2019)
Article
Mathematics, Applied
Zujin Zhang, Weihua Wang, Yong Zhou
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2019)
Article
Mathematics
Ahmad Mohammad Alghamdi, Sadek Gala, Maria Alessandra Ragusa, Zujin Zhang
Summary: This paper considers the 3D density-dependent magnetohydrodynamic equations with vacuum in the whole space R-3, and provides a regularity criterion involving the velocity field in BMO space norm. The work generalizes the regularity criterion of the constant density MHD equations to the density-dependent one.
BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY
(2021)
Article
Mathematics, Applied
Zujin Zhang
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2019)
Article
Mathematics, Applied
Zujin Zhang, Sinan Wang
APPLIED MATHEMATICS LETTERS
(2020)
Article
Mathematics, Applied
Zujin Zhang, Yali Zhang
Summary: It is proven that the solution to the Navier-Stokes system is smooth under specific conditions regarding the Sobolev spaces L-p and L-q, which improves upon previous research findings.
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
(2021)
Article
Mathematics, Applied
Jishan Fan, Zujin Zhang
Summary: This paper establishes regularity criteria for the density-dependent incompressible Boussinesq and liquid crystals model, with a key focus on the role of Kato-Ponce type commutator estimates.
ACTA APPLICANDAE MATHEMATICAE
(2021)
Article
Mathematics, Applied
Zujin Zhang, Sinan Wang
Summary: By estimating the nonlinear term in an innovative way, the optimal regularity criterion for shear thinning fluids can be obtained via the velocity field.
APPLIED MATHEMATICS LETTERS
(2021)
Article
Mathematics, Applied
Zujin Zhang, Caiyang Zeng
Summary: In this paper, the authors investigate a family of 3D models for the axisymmetric incompressible Navier-Stokes system by changing the strength of convection and adding a stirring force. The study shows global regularity when the strength of convection is stronger than that of the original Navier-Stokes system, indicating a potential stabilization effect of convection. This result addresses an open problem in a previous study by Hou-Liu-Wang (Nonlinearity 31:1940-1954, 2018).
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
(2022)
Article
Mathematics, Applied
Zujin Zhang, Jinfan Rao
Summary: In this study, we investigate the globally well-posedness of the axisymmetric MHD system with nearly critical initial data having a special structure. It is proved that if the scaling-invariant norm parallel to ru(0)(theta)parallel to(L8) is sufficiently small, then this system is globally well-posed.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2022)
Article
Mathematics, Applied
Zujin Zhang, Chenxuan Tong
Summary: Studying the axisymmetric Navier-Stokes equations led to the formulation of a new inequality through refined test functions and re-scaling schemes. Further improvement was achieved by employing dimension reduction techniques.
APPLICATIONS OF MATHEMATICS
(2022)
Article
Mathematics
Zujin Zhang, Yali Zhang
Summary: This study presents several weighted regularity criteria for axisymmetric solutions to the three-dimensional magnetohydrodynamic equations, which can effectively describe the relationships between velocity and vorticity components.
ANNALES POLONICI MATHEMATICI
(2021)
Article
Mathematics, Applied
Zujin Zhang, Yali Zhang
Summary: Yamazaki observed that the third component b(3) of the magnetic field can be estimated by the corresponding component u(3) of the velocity field in a specific norm, leading to the establishment of regularity criteria. This paper points out that lambda can be greater than 6, allowing for improvements on previous results.
APPLICATIONS OF MATHEMATICS
(2021)
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)
