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
Fuyi Xu, Liening Qiao, Mingxue Zhang
Summary: The article focuses on the Cauchy problem of the Rayleigh-Benard convection model for the micropolar fluid in two dimensions. It proves the unique local solvability of smooth solutions when the system has only velocity dissipation, establishes a criterion for the breakdown of smooth solutions based on the maximum norm of the gradient of scalar temperature field, and demonstrates the global regularity of the system with zero angular viscosity.
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
(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
Mathematics, Applied
Haifeng Shang, Mengyu Guo
Summary: This paper studies the global regularity problem of the 2D micropolar Rayleigh-Benard problem with partial velocity dissipation and micro-rotational dissipation. By exploiting the system's special structure and using energy methods, the global well-posedness of classical solutions for this system is established.
APPLIED MATHEMATICS LETTERS
(2022)
Article
Mathematics
Rafael Granero-Belinchon, Stefano Scrobogna
Summary: This paper studies the motion of a surface gravity wave with viscosity and proves two well-posedness results. The local solvability in Sobolev spaces for arbitrary dissipation is established, as well as the global well-posedness in Wiener spaces for sufficiently large viscosity. These results provide the first rigorous proofs of well-posedness for the specific system modeling gravity waves with viscosity.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2021)
Article
Mathematics, Applied
Shinya Kinoshita
Summary: This paper addresses the Cauchy problem of the 2D Zakharov-Kuznetsov equation, proving bilinear estimates that establish local well-posedness in the Sobolev space H-s(R-2) for s > -1/4, with optimality up to the endpoint. By utilizing the nonlinear version of the classical Loomis-Whitney inequality and developing an almost orthogonal decomposition of resonant frequencies, global well-posedness in L-2(R-2) is obtained.
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE
(2021)
Article
Mathematics, Applied
Ming Wang
Summary: It is demonstrated that the BBM equation possesses well-posedness globally in the space l(q)L(2)(R) for all 2 <= q infinity, and locally in the space l(infinity)L(2)(R). This implies that the BBM equation is well-posed in larger spaces and improves upon previous results.
APPLIED MATHEMATICS LETTERS
(2022)
Article
Mathematics, Applied
Shinya Kinoshita
Summary: This paper focuses on the Cauchy problem of the modified Zakharov-Kuznetsov equation on R-d. The sharp estimate is proven when d = 2, implying local well-posedness in the Sobolev space H-s(R-2) for s >= 1/4. For d >= 3, the small data global well-posedness is established using U-p and V-p spaces in the scaling critical Sobolev space H-sc (R-d) where s(c) = d/2 - 1.
FUNKCIALAJ EKVACIOJ-SERIO INTERNACIA
(2022)
Article
Mathematics
Kenta Oishi, Yoshihiro Shibata
Summary: This paper investigates the motion of incompressible magnetohydrodynamics with resistivity in a domain bounded by a free surface, and proves local well-posedness in general settings of domains from a mathematical point of view. Solutions are obtained for the velocity and magnetic fields in an anisotropic space, with specific conditions on the parameters p and q. The results are based on the L-p-L-q maximal regularity theorem for the Stokes equations with free boundary conditions and for the magnetic field equations with transmission conditions.
Article
Mathematics, Applied
Xin Zhong
Summary: The paper establishes the global existence and uniqueness of strong solutions for nonhomogeneous magnetic Benard system with far field vacuum in the whole two-dimensional plane. It shows that the initial data can be arbitrarily large, and the effectiveness of the method relies heavily on the structure of the system under consideration and spatial dimension.
APPLICABLE ANALYSIS
(2023)
Article
Mathematics, Applied
Xinliang Li, Zhong Tan
Summary: This paper investigates the global existence and uniqueness of smooth solutions for a 3D damped micropolar Rayleigh-Benard convection system without heat diffusion.
APPLIED MATHEMATICS LETTERS
(2021)
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
Hong Chen, Xin Zhong
Summary: We investigate the Cauchy problem of the two-dimensional full compressible magnetohydrodynamic equations in the entire plane with zero density at infinity. Using the spatial weighted energy method, we establish the local existence and uniqueness of strong solutions, while allowing for vacuum states to exist.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2023)
Article
Mathematics
Bo Xia
Summary: This study demonstrates that the wave equation with power-type nonlinearity on a three-dimensional torus is ill posed even around relatively regular dynamics. The findings suggest that the initial datum ensemble can be used to measure the size of bad datum sets in terms of probability. Additionally, the work indicates that probabilistic solutions constructed in previous studies can only be well approximated by smooth solutions issued from certain regularized datum.
INTERNATIONAL MATHEMATICS RESEARCH NOTICES
(2021)
Article
Mathematics, Interdisciplinary Applications
Li Peng, Yong Zhou
Summary: This paper discusses the well-posedness and regularity results of weak solution for a fractional wave equation allowing that the coefficients may have low regularity. The analysis relies on mollification arguments, Galerkin methods, and energy arguments.
FRACTAL AND FRACTIONAL
(2022)
Article
Mathematics, Applied
Junfeng Cao, Ke Chen, Huan Han
Summary: This paper proposes a two-stage image segmentation model based on structure tensor and fractional-order regularization. In the first stage, fractional-order regularization is used to approximate the Hausdorff measure of the MS model. The solution is found using the ADI scheme. In the second stage, thresholding is used for target segmentation. The proposed model demonstrates superior performance compared to state-of-the-art methods.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Dylan J. Oliver, Ian W. Turner, Elliot J. Carr
Summary: This paper discusses a projection-based framework for numerical computation of advection-diffusion-reaction (ADR) equations in heterogeneous media with multiple layers or complex geometric structures. By obtaining approximate solutions on a coarse grid and reconstructing solutions on a fine grid, the computational cost is significantly reduced while accurately approximating complex solutions.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Nathan V. Roberts, Sean T. Miller, Stephen D. Bond, Eric C. Cyr
Summary: In this study, the time-marching discontinuous Petrov-Galerkin (DPG) method is applied to the Vlasov equation for the first time, using backward Euler for a Vlasov-Poisson discretization. Adaptive mesh refinement is demonstrated on two problems: the two-stream instability problem and a cold diode problem.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Yizhi Sun, Zhilin Sun
Summary: This work investigates the convexity of a specific class of positive definite probability measures and demonstrates the preservation of convexity under multiplication and intertwining product. The study reveals that any integrable function on an interval with a polynomial expansion of fast absolute convergence can be decomposed into a pair of positive convex interval probabilities, simplifying the study of interval distributions and discontinuous probabilistic Galerkin schemes.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Bhagwan Singh, Komal Jangid, Santwana Mukhopadhyay
Summary: This paper examines the prediction of bending characteristics of nanoscale materials using the Moore-Gibson-Thompson thermoelasticity theory in conjunction with the nonlocal strain gradient theory. The study finds that the stiffness of the materials can be affected by nonlocal and length-scale parameters, and the aspect ratios of the beam structure play a significant role in bending simulations.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Guoliang Wang, Bo Zheng, Yueqiang Shang
Summary: This paper presents and analyzes a parallel finite element post-processing algorithm for the simulation of Stokes equations with a nonlinear damping term, which integrates the algorithmic advantages of the two-level approach, the partition of unity method, and the post-processing technique. The algorithm generates a global continuous approximate solution using the partition of unity method and improves the smoothness of the solution by adding an extra coarse grid correction step. It has good parallel performance and is validated through theoretical error estimates and numerical test examples.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Hao Xu, Zeng-Qi Wang
Summary: Fluid flow control problems are crucial in industrial applications, and solving the optimal control of Navier-Stokes equations is challenging. By using Oseen's approximation and matrix splitting preconditioners, we can efficiently solve the linear systems and improve convergence.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Zhengya Yang, Xuejuan Chen, Yanping Chen, Jing Wang
Summary: This paper focuses on the high-order stable numerical solutions of the time-space fractional diffusion equation. The Fourier spectral method is used for spatial discretization and the Spectral Deferred Correction (SDC) method is used for numerical solutions in time. As a result, a high-precision numerical discretization scheme for solving the fractional diffusion equation is obtained, and the convergence and stability of the scheme are proved. Several numerical examples are presented to demonstrate the effectiveness and feasibility of the proposed numerical scheme.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
