Article
Mathematics, Applied
Jinyi Sun, Lingjuan Zou
Summary: The dissipative quasi-geostrophic equation with dispersive forcing is studied in this paper. By striking a new balance between the dispersive effects and the smoothing effects, the global well-posedness for the Cauchy problem of this equation is obtained for arbitrary initial data, given that the dispersive parameter is sufficiently large.
Article
Mathematics
Muhammad Zainul Abidin, Jiecheng Chen
Summary: This paper examines the generalized porous medium equation, obtaining global well-posedness results for small initial data in certain conditions, and demonstrating Gevrey class regularity of the solution.
Article
Mathematics
Muhammad Zainul Abidin, Jiecheng Chen
Summary: This paper studies the Cauchy problem of the incompressible fractional Navier-Stokes equations in critical variable exponent Fourier-Besov-Morrey space F.N-p(center dot),h(center dot),q(s(.))(R-3). Global well-posedness result is proved for small initial data belonging to a specific space, extending some recent work.
ACTA MATHEMATICA SCIENTIA
(2021)
Article
Mathematics, Applied
Tadahiro Oh, Yuzhao Wang
Summary: This study establishes the local and global well-posedness of the modified KdV equation in modulation spaces. For s >= 1/4 and 2 <= p < infinity, the mKdV equation shows local well-posedness in the modulation space M-s(2,p) (R) and achieves global well-posedness under the same conditions.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
(2021)
Article
Mathematics, Applied
Achraf Azanzal, Chakir Allalou, Said Melliani, Adil Abbassi
Summary: In this paper, we study the subcritical dissipative quasi-geostrophic equation and prove the existence of a unique global-in-time solution for small initial data belonging to a critical Fourier-Besov-Morrey space. We also show the asymptotic behavior of the global solution, where the norm of the solution decays to zero as time goes to infinity.
JOURNAL OF PARTIAL DIFFERENTIAL EQUATIONS
(2023)
Article
Mathematics
Eiichi Nakai, Yoshihiro Sawano
Summary: The paper describes the spaces of pointwise multipliers on Morrey spaces using Morrey spaces, their preduals, and vector-valued Morrey spaces introduced by Ho. It also covers weak Morrey spaces. The results of the paper complete the characterization of earlier works and show that different quasi-Banach lattices can create the same vector-valued Morrey spaces. The goal of the paper is to provide a comprehensive picture of the pointwise multiplier spaces.
Article
Mathematics
Jiahui Zhu, Xinyun Wang, Heling Su
Summary: In this paper, we examine a 2D stochastic quasi-geostrophic equation driven by jump noise in a smooth bounded domain. We prove the local existence and uniqueness of mild L-p(D)-solutions for the dissipative quasi-geostrophic equation with a full range of subcritical powers alpha is an element of (1/2,1] by employing the semigroup theory and fixed point theorem. Our approach, which is based on the Yosida approximation argument and Ito formula for the Banach space valued processes, enables us to establish some uniform bounds for the mild solutions. Furthermore, we prove the global existence of mild solutions in L-infinity(0,T;L-p(D)) space for all p > 2/2 alpha-1, consistent with the deterministic case.
Article
Mathematics
Diego Cordoba, Luis Martinez-Zoroa
Summary: In this paper, we investigate the construction of solutions with finite energy for the surface quasi-geostrophic equations. We show that these solutions, initially belonging to a certain function space, do not satisfy the requirements of that space for t > 0. We also prove a similar result for a specific range of function spaces and establish strong ill-posedness in the critical space.
ADVANCES IN MATHEMATICS
(2022)
Article
Mathematics, Applied
Hyungjun Choi
Summary: We prove the global regularity of smooth solutions for a dissipative surface quasi-geostrophic equation with both velocity and dissipation logarithmically supercritical compared to the critical equation. Our primary tool is the nonlinear maximum principle which provides transparent proofs of global regularity for nonlinear dissipative equations. We also prove an uniform-in-time gradient estimate for the critical and slightly supercritical SQG equation and establish the eventual exponential decay of the solutions.
Article
Mathematics
Daniel Oliveira da Silva, Alejandro J. Castro
Summary: This study establishes an asymptotic rate of decay for the spatial analyticity radius of solutions to the nonlinear wave equation with initial data in the analytic Gevrey spaces.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2021)
Article
Mathematics, Applied
Muhammad Zainul Abidin, Jie Cheng Chen
Summary: This paper considers a generalized incompressible magnetohydrodynamics system, and establishes the global well-posedness of the system with small initial condition in variable exponent Fourier-Besov-Morrey spaces using the Littlewood-Paley decomposition and Fourier localization method. Furthermore, it also achieves the Gevrey class regularity of the solution.
ACTA MATHEMATICA SINICA-ENGLISH SERIES
(2022)
Article
Mathematics, Applied
Yatao Li, Jitao Liu, Yanxia Wu
Summary: In this paper, we investigate the Cauchy problem of the inviscid lake equations in the Besov spaces for the first time and prove the global existence and uniqueness of the solutions.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2022)
Article
Mathematics, Applied
Mustapha Amara, Jamel Benameur
Summary: This paper proves the global existence of the two-dimensional anisotropic quasi-geostrophic equations under certain conditions in the specified Sobolev spaces. The proof is based on the Gevrey-class regularity of the solution near zero.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2022)
Article
Mathematics
Minjie Shan, Baoxiang Wang, Liqun Zhang
Summary: This article proves that the Cauchy problem for the Zakharov-Kuznetsov equation on R2 is globally well-posed for initial data in Hs space with s > -113. Since conservation laws are not valid in Sobolev spaces below L2, an almost conserved quantity is constructed using a multilinear correction term based on the I-method introduced by Colliander, Keel, Staffilani, Takaoka, and Tao. Unlike the KdV equation, the main challenge lies in handling the resonant interactions due to the multidimensional and multilinear nature of the problem. The proof relies on the bilinear Strichartz estimate and the nonlinear Loomis-Whitney inequality.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2023)
Article
Mathematics
Feng Liu, Shuai Xi, Zirong Zeng, Shengguo Zhu
Summary: This paper investigates the Cauchy problem of three-dimensional incompressible magnetohydrodynamic equations, providing uniform estimates for the coupling terms between the fluid and magnetic field under sufficiently small initial norms. Global-in-time wellposedness of mild solutions in Morrey spaces is established using these estimates, along with obtaining the asymptotic behaviors of the solutions.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2022)
