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Article
The global existence and analyticity of a mild solution to the 3D regularized MHD equations
In this paper, we study the three-dimensional regularized MHD equations with fractional Laplacians in the dissipative and diffusive terms. We establish the global existence of mild solutions to this system wit...
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Article
A general degenerate reaction-diffusion model for acid-mediated tumor invasion
In this paper, we continue the research in Li et al. (J Differ Equ 371:353–395, 2023) and study the linear and global stability of a class of reaction-diffusion systems with general degenerate diffusion. The e...
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The elliptic net algorithm revisited
Efficient implementation of pairings is a fundamental ingredient in pairing-based cryptographic protocols. The Elliptic Net algorithm is an alternative method to Miller’s algorithm for computing the (Optimal) ...
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Article
Global Well-Posedness and Optimal Time Decay Rates for the Compressible Oldroyd-B Model in \({\mathbb {R}}^2\)
This paper is devoted to the global well-posedness and the optimal time decay rates for the two-dimensional compressible Oldroyd-B model. By introducing new quantities, we find another better perturbation syst...
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The sharp time-decay rates for one-dimensional compressible isentropic Navier-Stokes and magnetohydrodynamic flows
In this paper, we investigate the large-time behavior of strong solutions to the Cauchy problem for one-dimensional compressible isentropic magnetohydrodynamic equations near a stable equilibrium. The differen...
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Article
Local existence for the non-resistive magnetohydrodynamic system with fractional dissipation in the \(L^p\) framework
In this paper, we consider the Cauchy problem of the d-dimensional magnetohydrodynamic (MHD) system with the fractional dissipation $$(-\Delta...
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Article
Global Well-Posedness and Decay Rates for the Three-Dimensional Compressible Phan-Thein–Tanner Model
In this paper, we are concerned with the global well-posedness and decay rates of strong solutions for the three-dimensional compressible Phan-Thein–Tanner model. We prove that this set of equations admits a u...
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Article
Global Well-posedness for the Three-Dimensional Generalized Phan–Thien–Tanner Model in Critical Besov Spaces
A new Generalized Phan–Thien–Tanner (GPTT) model is derived from a Lodge–Yamamoto type of network theory for the polymeric fluids. The GPTT model is developed to describe the rheological behavior of the viscoe...
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Article
Boundary layer problems for the two-dimensional inhomogeneous incompressible magnetohydrodynamics equations
In this paper, we study the well-posedness of boundary layer problems for the inhomogeneous incompressible magnetohydrodynamics (MHD) equations, which are derived from the two-dimensional density-dependent inc...
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Article
Open AccessLower bound of decay rate for higher-order derivatives of solution to the compressible fluid models of Korteweg type
This paper concerns the lower bound decay rate of global solution for compressible Navier–Stokes–Korteweg system in three-dimensional whole space under the ...
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Article
Global Existence and Optimal Convergence Rates of Solutions for Three-Dimensional Electromagnetic Fluid System
In this article, we study the electromagnetic fluid system in three-dimensional whole space ℝ3. Under assumption of small initial data, we establish the unique global solution by energy method. Moreover, we obtai...
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Optimal Decay Rate for the Compressible Flow of Liquid Crystals in \(L^p\) Type Critical Spaces
The purpose of this paper is to establish the optimal time decay rate of solutions for the compressible flow of nematic liquid crystals in ...
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Article
Decay rates of higher-order norms of solutions to the Navier-Stokes-Landau-Lifshitz system
In this paper, we investigate a system of the incompressible Navier-Stokes equations coupled with Landau-Lifshitz equations in three spatial dimensions. Under the assumption of small initial data, we establish...
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Article
Global existence and incompressible limit in critical spaces for compressible flow of liquid crystals
The Cauchy problem for the compressible flow of nematic liquid crystals in the framework of critical spaces is considered. We first establish the existence and uniqueness of global solutions provided that the ...
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Article
Privacy-preserving outsourcing of image feature extraction in cloud computing
Private image data, especially including the biometric data with an authentication property, has received more and more attention along with the development of researches on big data. Consequently, to protect ...
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Complete weight enumerators of a family of three-weight linear codes
Linear codes have been an interesting topic in both theory and practice for many years. In this paper, for an odd prime p, we present the explicit complete weight enumerator of a family of p-ary linear codes cons...
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Global Cauchy problem for a Leray-α model
In this paper, we consider the Cauchy problem for the 3D Leray-α model, introduced by Cheskidov et al.[11]. We obtain the global solution for the 3D Leray-α model in the fractional index Sobolev space, and prove ...
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Article
A class of three-weight linear codes and their complete weight enumerators
Recently, linear codes constructed from defining sets have been investigated extensively and they have many applications. In this paper, for an odd prime p, we propose a class of p-ary linear codes by choosing a ...
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Article
Complete weight enumerators of some linear codes and their applications
Recently, linear codes constructed from defining sets have been extensively studied. It was shown that the linear codes may have a few nonzero weights or be optimal if the defining sets are well chosen. The we...
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Article
Optimal decay rates of classical solutions for the full compressible MHD equations
In this paper, we are concerned with optimal decay rates for higher-order spatial derivatives of classical solutions to the full compressible MHD equations in three-dimensional whole space. If the initial pert...
