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Teng-Fei Zhang

Publications and source records attributed to Teng-Fei Zhang.

14 recordsLinked to original sources
arXiv2026

Compressible Navier-Stokes-Landau-Lifshitz-Gilbert system: derivations and well-posedness

In this paper, we first derive the compressible Navier-Stokes/Landau-Lifshitz-Gilbert (NS-LLG) model for magnetoelastic materials via the energetic variational approach (EnVarA). It is important to emphasize that the manner in which the evolution of magnetoelastic materials is influenced by the fluid motion--specifically through the deformation gradient--determines the kinematics of the magnetization and consequently leads to distinct governing equations. Subsequently, we establish the local-in-time existence of solutions to the compressible NS-LLG system under finite initial energy. Finally, near the constant equilibrium for magnetoelasticity in the absence of an external magnetic field, we reformulate the evolutionary model, which allows an additional dissipative term to be identified from the elastic stress. Based on this reformulation, we justify the global well-posedness of the evolutionary magnetoelasticity system with zero external magnetic field, provided the initial data are sufficiently small. In particular, when the magnetic field $M$ vanishes, this model reduces to the viscoelastic model. Our results significantly relax the previous initial data requirements, only assume the most basic structural condition $ρ_{0} \operatorname{det} F_{0} = 1$.

math.AP↗
arXiv2023

From Kinetic Flocking Model of Cucker-Smale Type to Self-Organized Hydrodynamic model

We investigate the hydrodynamic limit problem for a kinetic flocking model. We develop a GCI-based Hilbert expansion method, and establish rigorously the asymptotic regime from the kinetic Cucker-Smale model with a confining potential in a mesoscopic scale to the macroscopic limit system for self-propelled individuals, which is derived formally by Aceves-Sánchez, Bostan, Carrillo and Degond (2019). In the traditional kinetic equation with collisions, for example, Boltzmann type equations, the key properties that connect the kinetic and fluid regimes are: the linearized collision operator (linearized collision operator around the equilibrium), denoted by $\mathcal{L}$, is symmetric, and has a nontrivial null space (its elements are called collision invariants) which include all the fluid information, i.e. the dimension of Ker($\mathcal{L}$) is equal to the number of fluid variables. Furthermore, the moments of the collision invariants with the kinetic equations give the macroscopic equations. The new feature and difficulty of the corresponding problem considered in this paper is: the linearized operator $\mathcal{L}$ is not symmetric, i.e. $\mathcal{L}\neq \mathcal{L}^*$, where $\mathcal{L}^*$ is the dual of $\mathcal{L}$. Moreover, the collision invariants lies in Ker($\mathcal{L}^*$), which is called generalized collision invariants (GCI). This is fundamentally different with classical Boltzmann type equations. This is a common feature of many collective motions of self-propelled particles with alignment in living systems, or many active particle system. Another difficulty (also common for active system) is involved by the normalization of the direction vector, which is highly nonlinear.

math.AP↗
arXiv2022

Hydrodynamic limit of the incompressible Navier-Stokes-Fourier-Maxwell System with Ohm's Law from the Vlasov-Maxwell-Boltzmann system: Hilbert expansion approach

We prove a global-in-time limit from the two-species Vlasov-Maxwell-Boltzmann system to the two-fluid incompressible Navier-Stokes-Fourier-Maxwell system with Ohm's law. Besides the techniques developed for the classical solutions to the Vlasov-Maxwell-Boltzmann equations in the past years, such as the nonlinear energy method and micro-macro decomposition are employed, key roles are played by the decay properties of both the electric field and the wave equation with linear damping of the divergence free magnetic field. This is a companion paper of [N. Jiang and Y.-L. Luo, \emph{Ann. PDE} 8 (2022), no. 1, Paper No. 4, 126 pp] in which Hilbert expansion is not employed.

math.AP↗
arXiv2021

Global Existence of Classical Solutions for a Reactive Polymeric Fluid near Equilibrium

In this paper, we study a new micro-macro model for a reactive polymeric fluid, which is derived recently in [Y. Wang, T.-F. Zhang, and C. Liu, \emph{J. Non-Newton. Fluid Mech.} 293 (2021), 104559, 13 pp], by using the energetic variational approach. The model couples the breaking/reforming reaction scheme of the microscopic polymers with other mechanical effects in usual viscoelastic complex fluids. We establish the global existence of classical solutions near the global equilibrium, in which the treatment on the chemo-mechanical coupling effect is the most crucial part. In particular, a weighted Poincaré inequality with a mean value is employed to overcome the difficulty that arises from the non-conservative number density distribution of each species.

math.AP↗
arXiv2021

On a Reversible Gray-Scott Type System from Energetic Variational Approach and Its Irreversible Limit

Most of the previous studies on the well-known Gray-Scott model view it as an irreversible chemical reaction system. In this paper, we derive a four-species reaction-diffusion system using the energetic variational approach based on the law of mass action. This is a reversible Gray-Scott type model, which has a natural entropy structure. We establish the local well-posedness of this system, and justify the limit to the corresponding irreversible Gray-Scott type system as some backward coefficients tend to zero. Furthermore, under some smallness assumption on the initial data, we obtain the global-in-time existence of classical solutions of the reversible system.

math.AP↗
arXiv2021

A two species micro-macro model of wormlike micellar solutions and its maximum entropy closure approximations: An energetic variational approach

Wormlike micelles are self-assemblies of polymer chains that can break and recombine reversibly. In this paper, we derive a thermodynamically consistent two species micro-macro model of wormlike micellar solutions by employing an energetic variational approach. The model incorporates a breakage and combination process of polymer chains into the classical micro-macro dumbbell model for polymeric fluids in a unified variational framework. We also study different maximum entropy closure approximations to the new model by "variation-then-closure" and "closure-then-variation" approaches. By imposing proper dissipation in the coarse-grained level, the closure model, obtained by "closure-then-approximation", preserves the thermodynamical structure of both mechanical and chemical parts of the original system. Several numerical examples show that the closure model can capture the key rheological features of wormlike micellar solutions in shear flows.

physics.flu-dyn↗
arXiv2020

Coupled Self-Organized Hydrodynamics and Navier-Stokes models: local well-posedness and the limit from the Self-Organized Kinetic-fluid models

A coupled system of self-organized hydrodynamics and Navier-Stokes equations (SOH-NS), which models self-propelled particles in a viscous fluid, was recently derived by Degond et al. \cite{DMVY-2017-arXiv}, starting from a micro-macro particle system of Vicsek-Navier-Stokes model, through an intermediate step of a self-organized kinetic-kinetic model by multiple coarse-graining processes. We first transfer SOH-NS into a non-singular system by stereographic projection, then prove the local in time well-posedness of classical solutions by energy method. Furthermore, employing the Hilbert expansion approach, we justify the hydrodynamic limit from the self-organized kinetic-fluid model to macroscopic dynamics. This provides the first analytically rigorous justification of the modeling and asymptotic analysis in \cite{DMVY-2017-arXiv}.

math.AP↗
arXiv2015

Hydrodynamic limits of the kinetic self-organized models

The self-organized hydrodynamic models can be derived from the kinetic version of the Vicsek model. The formal derivations and local well-posedness of the macroscopic equations are done by Degond and his collaborators. In this paper, we rigorously justify this hydrodynamic limit.

math.AP↗
arXiv2013

Gevrey Regularity for Solutions of the Non-Cutoff Boltzmann Equation: Spatially Inhomogeneous Case

In this paper we consider the non-cutoff Boltzmann equation in spatially inhomogeneous case. We prove the propagation of Gevrey regularity for the so-called smooth Maxwellian decay solutions to the Cauchy problem of spatially inhomogeneous Boltzmann equation, and obtain Gevrey regularity of order $1/(2s)$ in the velocity variable $v$ and order 1 in the space variable $x$. The strategy relies on our recent results for spatially homogeneous case (J. Diff. Equ. 253(4) (2012), 1172-1190. DOI: 10.1016/j.jde.2012.04.023). Rather, we need much more intricate analysis additionally in order to handle with the coupling of the double variables. Combining with the previous result mentioned above, it gives a whole characterization of the Gevrey regularity of the particular kind of solutions to the non-cutoff Boltzmann.

math.AP↗
arXiv2013

Gevrey Smoothing Effect of Solutions to Non-Cutoff Boltzmann Equation for Soft Potential with Mild and Critical Singularity

In this paper we study the Gevrey smoothing effect of solutions to the non-cutoff spatially homogeneous and inhomogeneous Boltzmann equation for soft potential. We consider the mild singularity case $s<1/2$ as we did in the previous work for spatially homogeneous case (J. Diff. Equ. 253(4) (2012), 1172-1190. DOI: 10.1016/j.jde.2012.04.023) and for spatially inhomogeneous case (arXiv:1304.2971), and try to extend the range of $γ$. We derive a new coercivity estimate for collision operator, using which we can obtain the Gevrey regularity for $γ\in (-5/2,0)$ improving the previous assumption $γ\in (-1-2s,0)$. Besides, we consider $γ$ and $s$ separately instead of viewing $γ+2s$ as one untied quantity.

math.AP↗
arXiv2012

Gevrey regularity of spatially homogeneous Boltzmann equation without cutoff

In this paper, we study the Gevrey regularity of spatially homogeneous Boltzmann equation without angular cutoff. We prove the propagation of Gevrey regularity for $C^\infty$ solutions with the Maxwellian decay to the Cauchy problem of spatially homogeneous Boltzmann equation. The idea we use here is based on the framework of Morimoto's recent paper (See Morimoto: J. Pseudo-Differ. Oper. Appl. (2010) 1: 139-159, DOI:10.1007/s11868-010-0008-z), but we extend the range of the index $γ$ satisfying $γ+ 2s \in (-1,1)$, $s\in (0,1/2)$ and in this case we consider the kinetic factor in the form of $Φ(v)=|v|^γ$ instead of $\la v \ra ^γ$ as Morimoto did before.

math.AP↗