Article
Mathematics
Lotfi Jlali
Summary: This paper examines the long time decay of global solutions to the 3D incompressible Navier-Stokes equations. The study shows that if u is a global solution under certain conditions, then the decay of u(t) to zero as time increases is proven, utilizing techniques based on Fourier analysis.
Article
Mathematics, Applied
Hongmin Li, Yuelong Xiao, Zhong Zhao
Summary: This paper investigates the decay of solutions to 3D Navier-Stokes equations with a nonlinear damping term, discussing the bounds and optimal decay rates of the global strong solutions in negative Sobolev and L2 spaces, as well as obtaining the upper bound of the derivative. Additionally, the asymptotic stability of the solutions to the system is investigated.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics
Masatoshi Okita
Summary: This paper proves that every smooth solution u(t, x) on (0, T) of incompressible Navier-Stokes equations on Rn can be extended beyond t > T if u(t, x) is an element of L-w(r)(0, T; L-sigma(p)) and satisfies a blow-up critical time order estimate.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2023)
Article
Mathematics, Applied
L. Rebholz, F. Tone
Summary: This paper studies the H1-stability of the BDF2 scheme for the 2D Navier-Stokes equations for all positive time. Specifically, we discretize in time using the backward differentiation formula (BDF2) and prove the stability of the numerical scheme with the help of the discrete Gronwall lemma and the discrete uniform Gronwall lemma.
APPLIED MATHEMATICS LETTERS
(2023)
Article
Mathematics
Shuichi Kawashima, Ryosuke Nakasato, Takayoshi Ogawa
Summary: The study focuses on the global existence of solution for the initial value problem of the compressible Hall-magnetohydrodynamic system in the whole space R-3, showing both the manner of existence and time decay of the solution. Results also demonstrate the pointwise estimate of the solution in the Fourier space, utilizing systematic use of product estimates in Chemin-Lerner spaces and applying the energy method by Matsumura-Nishida.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2022)
Article
Mathematics
Yanlin Liu
Summary: In this paper, we establish the global existence of smooth solutions to axisymmetric Navier-Stokes equations in certain critical spaces, provided that the swirl part of the initial velocity is sufficiently small.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2022)
Article
Mathematics, Applied
Eduard Feireisl, Young-Sam Kwon, Antonin Novotny
Summary: We have identified a class of maximal dissipative solutions for models of compressible viscous fluids that maximize the energy dissipation rate, and shown that any maximal dissipative solution approaches an equilibrium state for large times.
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
(2021)
Article
Mathematics, Applied
Ryosuke Nakasato
Summary: We investigate the initial value problem for the incompressible magnetohydrodynamic system with the Hall-effect. By establishing various type product estimates in space-time mixed spaces and smoothing estimates for the solution of the linear equation, we prove the existence of a global-in-time solution in L-p-type critical Fourier-Besov spaces for the perturbation from a constant equilibrium state.
JOURNAL OF EVOLUTION EQUATIONS
(2022)
Article
Mathematics, Applied
Juan Wang, Changguo Xiao, Yinghui Zhang
Summary: In this study, the optimal time decay rates of the solution and its spatial derivatives from one-order to the highest-order for the 3D compressible Navier-Stokes-Korteweg system are proved. The main novelty lies in obtaining optimal decay rates of the highest-order spatial derivative of the density and the high-frequency part of the highest-order spatial derivative of the velocity by carefully exploiting the regularity effect of the Korteweg term and making full use of low-frequency and high-frequency decomposition.
APPLIED MATHEMATICS LETTERS
(2021)
Article
Mathematics, Applied
Ruihong Ji, Ling Tian, Jiahong Wu
Summary: The study on the large-time behavior of solutions to the 3D incompressible anisotropic Navier-Stokes (ANS) equations is very recent. This paper focuses on the case when the spatial domain Omega is T-2 x R and shows that it has a different large-time behavior compared to the case when Omega is R-3. For any small initial velocity field u(0) in H-2(Omega), a unique global solution u that remains small in H-2(Omega) is obtained, and as t approaches infinity, the velocity field u converges exponentially fast to a nontrivial steady state, with the first two components given by the horizontal average of the first two components of u(0) and the third component vanishing.
Article
Mathematics, Applied
Irena Lasiecka, Buddhika Priyasad, Roberto Triggiani
Summary: The paper focuses on incompressible Navier-Stokes equations in 2 or 3 dimensions on a bounded domain, and achieves uniform stabilization of the N-S system using finite dimensional feedback controls in critical function spaces.
APPLIED MATHEMATICS AND OPTIMIZATION
(2021)
Article
Mathematics, Interdisciplinary Applications
Mongi Blel, Jamel Benameur
Summary: This study focuses on the uniqueness, continuity in L-2, and large-time decay properties of Leray solutions of the three-dimensional incompressible Navier-Stokes equations with a nonlinear exponential damping term.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2022)
Article
Mathematics
Lu Wang, Shuokai Yan, Qinghua Zhang
Summary: This paper focuses on the global existence and time-decay rates of the strong solution for the Boussinesq system with full viscosity in R-n for n >= 3. The global existence and uniqueness of the strong solution (theta, u) for the Boussinesq system are established under certain initial assumptions. The paper also provides estimates for the solution.
JOURNAL OF MATHEMATICS
(2023)
Article
Mathematics, Applied
Zefu Feng, Guangyi Hong, Changjiang Zhu
Summary: This paper concerns the large-time behavior of solutions to the compressible Navier-Stokes equations for ideal reacting gases. It establishes the asymptotic stability of the constant equilibrium state with strictly positive constant density, temperature, and vanishing velocity, mass fraction of the reactant under suitable small initial perturbation.
Article
Mathematics, Applied
Yanmin Mu
Summary: This paper investigates the decay estimates for the inhomogeneous incompressible Navier-Stokes Equations in R-3. The main challenge lies in the fact that the density p only possesses L-infinity norm. To overcome this difficulty, a new key quantity f (+infinity)(0) ||u||^2(L infinity)dt < +infinity is discovered.
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
(2023)
Article
Mathematics, Applied
Jamel Benameur, Moez Benhamed
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2015)
Article
Mathematics, Applied
Jamel Benameur, Lotfi Jlali
JOURNAL OF MATHEMATICAL FLUID MECHANICS
(2016)
Article
Mathematics
J. Benameur, R. Selmi
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY
(2012)
Article
Mathematics, Applied
Jamel Benameur
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2013)
Article
Mathematics, Applied
Jamel Benameur, Ridha Selmi
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2014)
Article
Mathematics, Applied
Jamel Benameur
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
(2014)
Article
Mathematics
Jamel Benameur, Mongi Blel
Article
Mathematics, Applied
Jamel Benameur, Mongi Blel
JOURNAL OF FUNCTION SPACES
(2014)
Article
Mathematics, Applied
Jamel Benameur, Hajer Orf
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2019)
Article
Mathematics, Applied
Jamel Benameur, Mariem Bennaceur
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2020)
Article
Mathematics
Jamel Benameur, Lotfi Jlali
MATHEMATICA SLOVACA
(2020)
Article
Mathematics, Applied
Jamel Benameur, Saber Ben Abdallah
Summary: This paper demonstrates the global existence and analyticity of critical dissipative quasi-geostrophic equations under certain conditions, with the solution remaining regular. Fourier analysis and standard techniques were employed in the study.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2021)
Article
Mathematics, Interdisciplinary Applications
Mongi Blel, Jamel Benameur
Summary: This study focuses on the uniqueness, continuity in L-2, and large-time decay properties of Leray solutions of the three-dimensional incompressible Navier-Stokes equations with a nonlinear exponential damping term.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2022)
Article
Mathematics, Applied
Jamel Benameur, Lotfi Jlali
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS
(2016)
Article
Mathematics, Applied
Geunsu Choi, Mingu Jung, Sun Kwang Kim, Miguel Martin
Summary: This paper studies weak-star quasi norm attaining operators and proves that the set of such operators is dense in the space of bounded linear operators regardless of the choice of Banach spaces. It is also shown that weak-star quasi norm attaining operators have distinct properties from other types of norm attaining operators, although they may share some equivalent properties under certain conditions.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Maria Lorente, Francisco J. Martin-Reyes, Israel P. Rivera-Rios
Summary: In this paper, we provide quantitative one-sided estimates that recover the dependences in the classical setting. We estimate the one-sided maximal function in Lorentz spaces and demonstrate the applicability of the conjugation method for commutators in this context.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Fernando Cobos, Luz M. Fernandez-Cabrera
Summary: We provide a necessary and sufficient condition for the weak compactness of bilinear operators interpolated using the real method. However, this characterization does not hold for interpolated operators using the complex method.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Ovgue Gurel Yilmaz, Sofiya Ostrovska, Mehmet Turan
Summary: The Lupas q-analogue Rn,q, the first q-version of the Bernstein polynomials, was originally proposed by A. Lupas in 1987 but gained popularity 20 years later when q-analogues of classical operators in approximation theory became a focus of intensive research. This work investigates the continuity of operators Rn,q with respect to the parameter q in both the strong operator topology and the uniform operator topology, considering both fixed and infinite n.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
M. Agranovsky, A. Koldobsky, D. Ryabogin, V. Yaskin
Summary: This article modifies the concept of polynomial integrability for even dimensions and proves that ellipsoids are the only convex infinitely smooth bodies satisfying this property.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Abel Komalovics, Lajos Molnar
Summary: In this paper, a parametric family of two-variable maps on positive cones of C*-algebras is defined and studied from various perspectives. The square roots of the values of these maps under a faithful tracial positive linear functional are considered as a family of potential distance measures. The study explores the problem of well-definedness and whether these distance measures are true metrics, and also provides some related trace characterizations. Several difficult open questions are formulated.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Frederic Bayart
Summary: The passage describes the construction of an operator on a separable Hilbert space that is 5-hypercyclic for all δ in the range (ε, 1) and is not 5-hypercyclic for all δ in the range (0, ε).
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Helene Frankowska, Nikolai P. Osmolovskii
Summary: This paper investigates second-order optimality conditions for the minimization problem of a C2 function f on a general set K in a Banach space X. Both necessary and sufficient conditions are discussed, with the sufficiency condition requiring additional assumptions. The paper demonstrates the validity of these assumptions for the case when the set K is an intersection of sets described by smooth inequalities and equalities, such as in mathematical programming problems. The novelty of the approach lies in the arbitrary nature of the set K and the straightforward proofs.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Ole Fredrik Brevig, Kristian Seip
Summary: This paper studies the Hankel operator on the Hardy space and discusses its minimal and maximal norms, as well as the relationship between the maximal norm and the properties of the function.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Alexander Meskhi
Summary: Rubio de Francia's extrapolation theorem is established for new weighted grand Morrey spaces Mp),lambda,theta w (X) with weights w beyond the Muckenhoupt Ap classes. This result implies the one-weight inequality for operators of Harmonic Analysis in these spaces for appropriate weights. The necessary conditions for the boundedness of the Hardy-Littlewood maximal operator and the Hilbert transform in these spaces are also obtained. Some structural properties of new weighted grand Morrey spaces are investigated. Problems are studied in the case when operators and spaces are defined on spaces of homogeneous type.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Maud Szusterman
Summary: In this work, the necessary conditions on the structure of the boundary of a convex body K to satisfy all inequalities are investigated. A new solution for the 3-dimensional case is obtained in particular.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Rami Ayoush, Michal Wojciechowski
Summary: In this article, lower bounds for the lower Hausdorff dimension of finite measures are provided under certain restrictions on their quaternionic spherical harmonics expansions. This estimate is analogous to a result previously obtained by the authors for complex spheres.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
F. G. Abdullayev, V. V. Savchuk
Summary: This paper investigates the convergence and theorem proof of the Takenaka-Malmquist system and Fejer-type operator on the unit circle, and provides relevant results on the class of holomorphic functions representable by Cauchy-type integrals with bounded densities.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Sofiya Ostrovska, Mikhail I. Ostrovskii
Summary: This work aims to establish new results on the structure of transportation cost spaces. The main outcome of this paper states that if a metric space X contains an isometric copy of L1 in its transportation cost space, then it also contains a 1-complemented isometric copy of $1.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
Article
Mathematics, Applied
Pilar Rueda, Enrique A. Sanchez Perez
Summary: We prove a factorization theorem for Lipschitz operators acting on certain subsets of metric spaces of measurable functions and with values on general metric spaces. Our results show how a Lipschitz operator can be extended to a subset of other metric space of measurable functions that satisfies the following optimality condition: it is the biggest metric space, formed by measurable functions, to which the operator can be extended preserving the Lipschitz constant. Also, we demonstrate the coarsest metric that can be given for a metric space in which an order bounded lattice-valued-Lipschitz map is defined, and provide concrete examples involving the relevant space L0(mu).
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
