Article
Mathematics
Fucai Li, Yue Li, Baoyan Sun
Summary: In this paper, a quantum kinetic-fluid model in a three-dimensional torus is studied. The model is a combination of the Vlasov-Fokker-Planck equation and the compressible quantum Navier-Stokes equations with degenerate viscosity. A global weak solution to this model is established for arbitrarily large initial data when the pressure takes a specific form.
ACTA MATHEMATICA SCIENTIA
(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)
Review
Biochemical Research Methods
Yoonseok Park, Ted S. Chung, John A. Rogers
Summary: Recent advances in bio-interface technologies have provided a wide range of options for probing and modulating the behaviors of smallscale three dimensional biological constructs. Some effective design strategies in this emerging field of bioelectronics include thin deformable sheets, filamentary penetrating pins, open mesh structures and 3D interconnected networks. Multimodal interfaces, such as tissue-embedding scaffolds and tissue-surrounding frameworks, are highlighted in this review.
CURRENT OPINION IN BIOTECHNOLOGY
(2021)
Article
Mathematics, Applied
Xiaofeng Hou, Hongyun Peng
Summary: This paper investigates the existence of global classical solution to the Cauchy problem for the three-dimensional micropolar fluid equations with vacuum. The global classical solution is obtained when the far-field density is vacuum under certain assumptions, improving upon previous results.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2021)
Article
Mathematics
Ke Chen, Jie Liu
Summary: In this study, we construct weak solutions with finite kinetic energy to the 3D hypoviscous incompressible elastodynamics, which was previously unknown in the literature. Our result holds for fractional hypoviscosity (-delta)(theta), where 0 <= theta < 1. The proof is based on a convex integration scheme and suitable temporal correctors, inspired by the inherent geometric structure of the viscoelastic equations.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2022)
Article
Mathematics, Applied
L. Fang, Z. H. E. N. H. U. A. Guo
Summary: This paper investigates the existence of global weak solutions to a compressible non-Newtonian fluid with a power-law type. The main contribution lies in handling the power-law structure with a specific exponent while the pressure is related to rho(gamma) with gamma > 1. The existence of global weak solutions is proven using the Faedo-Galerkin method, weak compactness techniques, and the monotonicity method, inspired by the weak formulation of the momentum equation.
COMMUNICATIONS IN MATHEMATICAL SCIENCES
(2022)
Article
Mathematics, Applied
Huihui Zeng
Summary: This study successfully proves the almost global existence of smooth solutions for the three-dimensional vacuum free boundary problem with physical singularity under certain conditions, and establishes the relationship between the initial perturbation size and the existence time of smooth solutions. The key issue lies in the slow sub-linear growth of vacuum boundaries and the comparison with existing theories of expanding solutions in problems with physical singularity.
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
(2021)
Article
Computer Science, Interdisciplinary Applications
Cristian Mejia, Deane Roehl, Julio Rueda, Roberto Quevedo
Summary: This paper proposes a new embedded fracture approach for fluid flow in highly fractured porous media, which includes condensation technique to merge fracture contributions into continuum elements and guarantee compatibility between fractures and porous matrix within a standard finite element mesh. Despite its simplicity, the method demonstrates robustness and applicability to highly fractured rock reservoir cells with random fracture orientation. The pore pressure field obtained with this approach closely matches predictions from explicit approaches with zero-thickness interface elements, showing promising results.
COMPUTERS AND GEOTECHNICS
(2021)
Article
Mathematics, Applied
Qionglei Chen, Xiaonan Hao
Summary: The global well-posedness of the three-dimensional chemotaxis Navier-Stokes equations with a class of large initial data slowly varying in one direction is investigated in this study. The proof utilizes the special coupling structure of the system and localization technique in Fourier spaces. This research is copyrighted by Elsevier Ltd.
APPLIED MATHEMATICS LETTERS
(2021)
Article
Physics, Mathematical
Hailong Ye, Chunhua Jin
Summary: This paper studies the time periodic problem of a three-dimensional chemotaxis-Stokes model with porous medium diffusion δn(m) and inhomogeneous mixed boundary conditions. By using a double-level approximation method and some iterative techniques, the existence and time-space uniform boundedness of weak time periodic solutions for any m > 1 are obtained. Moreover, the regularity is improved for m <= 4/3 and it is shown that the obtained periodic solutions are, in fact, strong periodic solutions.
JOURNAL OF MATHEMATICAL PHYSICS
(2022)
Article
Mathematics
Guochun Wu, Lei Yao, Yinghui Zhang
Summary: In this paper, we study a compressible two-fluid model with common pressure and prove the global existence and long-time behavior of its classical solutions by exploiting the dissipation structure of the model and making use of key observations. This is the first result on the global existence of classical solutions to this model.
MATHEMATISCHE ANNALEN
(2023)
Article
Mathematics, Applied
Ping Hong, Xiaofeng Hou
Summary: In this paper, a new blowup criterion is established for the strong solution to the three-dimensional micropolar fluid equations with vacuum in a bounded domain. The blowup criterion is obtained in terms of BMOx norm of P and is independent of the velocity of rotation of the microscopic particles. The presence of vacuum is also allowed.
APPLIED MATHEMATICS LETTERS
(2023)
Article
Physics, Mathematical
Feng Dai, Bin Liu
Summary: This paper examines a haptotaxis model for cancer invasion in three dimensions without cell proliferation. By constructing an energy-functional, the paper overcomes mathematical difficulties and establishes the global existence of weak solutions to the associated initial-boundary value problem. This result has significant implications for research in this field.
JOURNAL OF MATHEMATICAL PHYSICS
(2022)
Article
Physics, Fluids & Plasmas
Patrick Charbonneau, Peter K. Morse, Will Perkins, Francesco Zamponi
Summary: Based on results from physics and mathematics literature, three scenarios for the fate of hard sphere crystallization in high dimensions are formulated, with scenario C being the most likely according to the investigation of densest sphere packings.
Article
Mathematics, Applied
Yi Zhu
Summary: This paper proves the global existence of general small solutions to compressible viscoelastic system, while removing the previous assumptions on initial state and structure, broadening the class of solutions. A new effective flux is introduced, and the wildest nonlinear term is regarded as linear term.
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
(2022)
Article
Mathematics, Applied
Hui Chen, Daoyuan Fang, Ting Zhang
Summary: This paper investigates the 3D Navier-Stokes equations in the whole space, introducing new inequalities and a priori estimates to provide critical regularity criteria. The range of q is extended while the solution is axisymmetric.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Mathematics
Xuan Liu, Ting Zhang
Summary: This paper investigates the well-posedness of the inhomogeneous nonlinear biharmonic Schrodinger equation with a spatial inhomogeneity coefficient K(x) behaving like vertical bar x vertical bar(-b) for 0 < b < min {N/2, 4}. The local well-posedness is demonstrated in the whole H-s-subcritical case, with 0 < s <= 2. The difficulties of the problem are addressed by deriving bilinear Strichartz's type estimates for the nonlinear biharmonic Schrodinger equations in Besov spaces.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2021)
Article
Mathematics, Applied
Yu Liu, Ting Zhang
Summary: In this paper, we define a renormalized dissipative measure-valued (rDMV) solution for the compressible magnetohydrodynamics (MHD) equations with non-monotone pressure law. We prove the existence of this rDMV solution and establish a suitable relative energy inequality. Additionally, we obtain the weak (measure-valued)-strong uniqueness property of this rDMV solution by utilizing the relative energy inequality.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
(2022)
Article
Mathematics, Applied
Hui Chen, Chenyin Qian, Ting Zhang
Summary: In this paper, we study the 3D MHD equations with equal viscosity and resistivity coefficients. We demonstrate that the suitable weak solution is regular at the origin (0, 0) when specific conditions are imposed on the velocity and magnetic fields components.
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
(2022)
Article
Mathematics, Applied
Hui Chen, Tai-Peng Tsai, Ting Zhang
Summary: This article investigates a new local regularity criterion for axisymmetric solutions of the 3D Navier-Stokes equations. The criterion is slightly supercritical and provides an upper bound for the oscillation of Gamma = ru(theta), which has a linear relationship with the logarithm of r.
COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS
(2022)
Article
Mathematics, Applied
Lihuai Du, Ting Zhang
Summary: This paper considers the stochastic Boussinesq equations with additive noise and proves the global existence of the strong solution in the case of strong stable stratification. The averaging theorem is also established.
JOURNAL OF MATHEMATICAL FLUID MECHANICS
(2022)
Article
Mathematics
Chenyin Qian, Hui Chen, Ting Zhang
Summary: In this paper, the global existence of weak solutions and the lifespan of strong solutions to the 3D inhomogeneous incompressible asymmetric fluids equations are studied. The energy method and the decomposing technique are used to obtain global Fujita-Kato solutions for the asymmetric fluids. The estimate of the lifespan of strong solutions to the 3D inhomogeneous incompressible asymmetric fluids equations is also investigated.
MATHEMATISCHE ANNALEN
(2023)
Article
Mathematics, Applied
Jiayan Wu, Ting Zhang
Summary: This paper obtains the nth-logarithmically improved regularity criterion of smooth solutions for the incompressible Leray-alpha-MHD model and establishes the new logarithmically improved regularity criterion for the 3D Navier-Stokes equation. Especially, a new logarithmically improved Serrin's criterion for the 3D Navier-Stokes equations is explored.
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
(2022)
Article
Mathematics, Applied
Jiayan Wu, Meng Qu, Jingjing Zhang, Ting Zhang
Summary: In this paper, equations involving a nonlocal operator are considered and some maximum principles are established. These principles are applied to solve the monotonicity and symmetry problems of semilinear equations and generalized Schrodinger equations.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Applied
Yanyan Li, Jingjing Zhang, Ting Zhang
Summary: In this paper, we demonstrate asymptotic stability of Landau solutions to the Navier-Stokes system under L-3 perturbations. We establish the local well-posedness of solutions to the perturbed system with initial data in the L-sigma (3) space, and global well-posedness with small initial data in the L-sigma (3) space, while also studying L-q decay for all q>3. We further investigate the local well-posedness, global well-posedness, and stability in L-p spaces for 3 < p < infinity.
JOURNAL OF MATHEMATICAL FLUID MECHANICS
(2023)
Article
Physics, Mathematical
Jingjing Zhang, Ting Zhang
Summary: In this paper, we study the global well-posedness of the perturbed Navier-Stokes equations around the Landau solution with small initial data in the X-1 space, which is defined as the space of distributions whose Fourier transform is integrable with a certain decay condition.
JOURNAL OF MATHEMATICAL PHYSICS
(2023)
Article
Mathematics
Yige Bai, Ting Zhang
Summary: In this paper, the authors investigate the Cauchy problem of the 3D compressible viscoelastic hydrodynamic model. They decompose the fluid equations and use Duhamel's principle to derive the expression of the corresponding solution. By refined integral calculation and classification discussion, they analyze the interaction of different waves in detail and obtain the pointwise time-space estimates of the solutions.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2023)
Article
Physics, Mathematical
Yu Liu, Song Meng, Jiayan Wu, Ting Zhang
Summary: This paper focuses on compressible viscoelastic flows of the Oldroyd type with a general pressure law, where one of the non-Newtonian fluids exhibits elastic behavior. For these flows, the authors prove the global existence and uniqueness of a strong solution in critical Besov spaces. The proof does not require any compatible conditions, and the authors also obtain the optimal decay rates of the solution in the Besov spaces.
JOURNAL OF MATHEMATICAL PHYSICS
(2023)
Article
Mathematics, Applied
Xuan Liu, Ting Zhang
Summary: We study the asymptotic behavior of the modified two-dimensional Schrodinger equation in the critical regime and prove global-in-time solution for any smooth initial datum of small size. We also provide pointwise decay estimates and large time asymptotic formulas for the solution.
Article
Mathematics, Applied
Xuan Liu, Ting Zhang
Summary: This paper investigates the local well-posedness and blow-up properties of the fourth-order Schrödinger equation.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
(2022)
