Article
Mathematics, Applied
Zhengguang Guo, Yafei Li, Zdenek Skalak
Summary: This paper establishes new regularity criteria for the three-dimensional incompressible MHD equations using partial components of velocity and magnetic fields, and also obtains some Prodi-Serrin type regularity conditions.
JOURNAL OF MATHEMATICAL FLUID MECHANICS
(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
Diego Chamorro, Jiao He
Summary: The use of Morrey spaces in parabolic generalization is crucial for studying the regularity theory of both classical Navier-Stokes equations and MHD equations.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2021)
Article
Multidisciplinary Sciences
Maria Alessandra Ragusa, Fan Wu
Summary: This paper investigates the regularity of weak solutions to the 3D incompressible MHD equations, providing a regularity criterion for weak solutions involving any two groups of functions in anisotropic Lorentz space.
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
Qionglei Chen, Zhen Li
Summary: By utilizing Fourier analysis and the equation's structure, we investigate the blow-up criterion of the smooth solution for the 3D Boussinesq system with partial viscosity.
APPLIED MATHEMATICS LETTERS
(2022)
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
Zhengguang Guo, Fangru Chen
Summary: This paper investigates the regularity conditions of axisymmetric weak solutions to the three-dimensional incompressible magnetohydrodynamics equations with nonzero swirl component. By utilizing the Littlewood-Paley decomposition techniques, it is shown that weak solutions become regular if the swirl component of vorticity satisfies certain conditions. This result provides a positive answer to the marginal case for the regularity of MHD equations.
MATHEMATISCHE NACHRICHTEN
(2023)
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
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
Xuanji Jia
Summary: This paper studies the 3D generalized magnetohydrodynamics (gMHD) equations with dissipation terms. It is proved that a weak solution (u, b) to gMHD equations is smooth on 1[83 x (0, T] if u, Vu or (- increment )m/2u belongs to Lq(0,T; Lp(1[83)) with p, q and m = min{& alpha;, & beta;} satisfying the generalized Ladyzhenskaya-Prodi-Serrin type conditions.
APPLIED MATHEMATICS LETTERS
(2023)
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
Chuong Tran
Summary: This article discusses Leray's criterion for singularity in the Navier-Stokes equations, examines the necessary conditions and constraints for singularity, and derives the logarithmic constraint on divergence related to Leray's scaling.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2022)
Article
Mathematics
J. Bravo-Olivares, E. Fernandez-Cara, E. Notte-Cuello, M. A. Rojas-Medar
Summary: This study extends the spectral regularity criteria of the Prodi-Serrin kind to the MHD equations, demonstrating that the finiteness of the Prodi-Serrin norm of xN implies the regularity of the weak solution (u, h), without any restriction on the magnetic field.
ELECTRONIC RESEARCH ARCHIVE
(2022)
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
F. Deringoz, V. S. Guliyev, M. N. Omarova, M. A. Ragusa
Summary: This paper investigates the boundedness of Calderon-Zygmund operators and their commutators in generalized weighted Orlicz-Morrey spaces, as well as the boundedness in the vector-valued setting.
BULLETIN OF MATHEMATICAL SCIENCES
(2023)
Article
Mathematics, Applied
Maria Alessandra Ragusa, Abdolrahman Razani, Farzaneh Safari
Summary: In this study, a variational principle is used to examine a Muckenhoupt weighted p-Laplacian equation on the Heisenberg groups. The existence of at least one positive radial solution to the problem under the Dirichlet boundary condition in the first order Heisenberg-Sobolev spaces is proven.
Article
Mathematics
Ravi P. Agarwal, Ahmad M. Alghamdi, Sadek Gala, Maria Alessandra Ragusa
Summary: In this paper, we establish a regularity criterion for micropolar fluid flows by introducing the one component of the velocity in critical Morrey-Campanato space. Specifically, we prove that if Z0 T 24 9 symbolscript < infinity, where 0 < r < M2, 3 10, r, then the weak solution (u, w) is regular.
MATHEMATICAL MODELLING AND ANALYSIS
(2023)
Article
Mathematics, Applied
Munirah Alotaibi, Mohamed Jleli, Maria Alessandra Ragusa, Bessem Samet
Summary: This paper investigates an initial value problem for a nonlinear time-fractional Schrodinger equation with a singular logarithmic potential term. The problem involves the left/forward Hadamard-Caputo fractional derivative with respect to the time variable. Sufficient criteria for the absence of global weak solutions are obtained using the test function method with a judicious choice of the test function.
APPLICABLE ANALYSIS
(2023)
Article
Mathematics
Long Le Dinh, Duc Phuong Nguyen, Maria Alessandra Ragusa
Summary: This paper aims to retrieve the initial value for a non-local fractional Sobolev-Galpern problem. The Fourier truncation method is applied to construct the regularized solution, and the convergence between the solution and the regularized solution is estimated. Additionally, a numerical example is proposed to assess the efficiency of the theory.
BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY
(2023)
Article
Mathematics, Applied
Hamza Boujemaa, Badr Oulgiht, Maria Alessandra Ragusa
Summary: This paper introduces a new class of fractional Orlicz-Sobolev space with variable-order. The basic properties of this space are given and some compactness results are proved. Then, using techniques of calculus of variations combined with the theory of Musielak functions, the existence of a nonnegative weak solution for a singular elliptic type problem in a fractional variable-order Orlicz-Sobolev space with homogeneous Dirichlet boundary conditions is proved. (c) 2023 Elsevier Inc. All rights reserved.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2023)
Article
Mathematics, Applied
Nabil Chems Eddine, Phuong Duc Nguyen, Maria Alessandra Ragusa
Summary: In this article, the existence and infinitely many nontrivial solutions for a class of nonlinear critical anisotropic elliptic equations involving variable exponents and two real parameters are obtained by combining the variational method and the concentration-compactness principle.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Applied
V. S. Guliyev, Meriban N. N. Omarova, Maria Alessandra Ragusa
Summary: In this article, the continuity of commutators [b, T] of Calderón-Zygmund operators with BMO functions in generalized Orlicz-Morrey spaces M-F, M-f(R-n) is demonstrated. Necessary and sufficient conditions for the boundedness of the genuine Calderón-Zygmund operators T and their commutators [b, T] on generalized Orlicz-Morrey spaces are provided.
ADVANCES IN NONLINEAR ANALYSIS
(2023)
Article
Mathematics
Ravi P. Agarwal, Ahmad M. Alghamdi, Sadek Gala, Maria Alessandra Ragusa
Summary: In this article, the regularity criteria for weak solutions of the Boussinesq equations are studied, focusing on the horizontal component of velocity or the horizontal derivatives of the two components of velocity in anisotropic Lorentz spaces. The results highlight the dominant role of the velocity field in the regularity theory of the Boussinesq equations.
DEMONSTRATIO MATHEMATICA
(2023)
Article
Mathematics, Applied
Ines Ben Omrane, Mourad Ben Slimane, Sadek Gala, Maria Alessandra Ragusa
Summary: This paper investigates the regularity criteria for the 3D micropolar fluid equations in terms of pressure in weak Lebesgue space. It is proven that the weak solution is regular on (0, T] if the pressure satisfies either the norm IIπIILα,∞(0,T;Lβ,∞(R3)) with 2α+β/3=2 and 32<β<∞ or IIVπIILα,∞(0,T;Lβ,∞(R3)) with 2α+β/3=3 and 1<β<∞ is sufficiently small.
Article
Mathematics, Applied
Ben Omrane Ines, Gala Sadek, Ragusa Maria Alessandra
Summary: This paper studies the logarithmically improved regularity criterion of the 3D Boussinesq equations using the middle eigenvalue of the strain tensor in Besov spaces with negative indices. It shows that a weak solution becomes regular on (0, T] if the given inequality holds for some 0 < δ < 1. This result improves upon the previous works by Neustupa-Penel and Miller.
EVOLUTION EQUATIONS AND CONTROL THEORY
(2023)
Article
Mathematics, Applied
Hamdy M. Ahmed, A. M. Sayed Ahmed, Maria Alessandra Ragusa
Summary: By using Monch fixed point theorem, fractional calculus, and stochastic analysis, this paper establishes sufficient conditions for the existence of solutions to non-instantaneous impulsive Hilfer-Katugampola fractional differential equations of order 1/2 < alpha < 1 and parameter 0 <= beta <= 1 with fractional Brownian motion (fBm), Poisson jumps, and nonlocal conditions. An example is provided to illustrate the obtained results.
TWMS JOURNAL OF PURE AND APPLIED MATHEMATICS
(2023)
Article
Mathematics
Aidyn Kassymov, Maria Alessandra Ragusa, Michael Ruzhansky, Durvudkhan Suragan
Summary: In this study, we establish the Adams type Stein-Weiss inequality on general homogeneous groups and demonstrate its applications on Morrey spaces. These results are not only new for general homogeneous groups, but also for the Euclidean space.
JOURNAL OF FUNCTIONAL ANALYSIS
(2023)
Article
Mathematics, Applied
Mohamed Jleli, Maria Alessandra Ragusa, Bessem Samet
Summary: This paper studies differential inequalities of a specific form and establishes necessary conditions for the existence of nontrivial weak solutions. The proof is based on the nonlinear capacity method and a result by Bianchi and Setti (2018).
ADVANCES IN DIFFERENTIAL EQUATIONS
(2023)
Article
Multidisciplinary Sciences
John Augustine, Khalid Hourani, Anisur Rahaman Molla, Gopal Pandurangan, Adi Pasic
Summary: We study scheduling mechanisms that balance the containment of COVID-19 spread and in-person activity in organizations. Our group scheduling mechanisms randomly partition the population into groups and schedule their work days with possible gaps. We demonstrate through theoretical analysis and extensive simulations that our mechanisms effectively control the virus spread while maintaining a certain level of in-person activity.