arXiv subjects

Tianfang Wu

Publications and source records attributed to Tianfang Wu.

4 recordsLinked to original sources

arXiv2026

Nonlinear Stability of Taylor-Couette Flows with Heat Buoyancy

This paper investigates the nonlinear stability of Taylor-Couette (TC) flows incorporating the thermal buoyancy within an annular domain characterized by small viscosity $ν$ and thermal diffusivity $μ$. It is well established that the buoyancy induced convection significantly impacts practical industrial applications of Taylor-Couette flow \cite{Chen2006}. In contrast to \cite{An.2024}, we specifically examines the influence of the temperature gradients and the gravity on the stability of Taylor-Couette flows in this article. The thermal buoyancy term introduces a destabilizing radial derivative $\partial_r$ into the rotating TC system. To mitigate this destabilizing effect, we employ estimates involving the negative derivatives. Consequently, the additional viscous damping becomes necessary to counterbalance the buoyancy induced instability. Our stability criterion requires that the initial perturbations from the Taylor-Couette flow are bounded by a suitable power of the viscosity. Under this condition, we prove that solutions to the 2D Boussinesq system on $[1, R] \times \mathbb{S}^1$ remain close to the Taylor-Couette flow at the same order.

math.AP↗

arXiv2026

Acoustic limit of Boltzmann equations for gas mixture

In this paper, we study the hydrodynamic and acoustic limit from Boltzmann equations for two species gas mixture with potential $γ\in \left(-3, 1\right]$. % in the whole space $(x \in \mathbb{R}^3)$.Here the particle masses are different which derives to the loss of symmetry to the linearized collision operator. %This paper resolves it precisely by using a framework based on vector-valued functions. We construct the hydrodynamic limit for two species based on the Hilbert expansion method when the Knudsen number is small. The key observation is the precise properties of the linearized collision operators, including the extra operators due to the different particle masses $(m^A \neq m^B)$. In additional, the acoustic limit of the Boltzmann equations for gas mixtures is rigorously justified by assuming the strength of the initial data depends on the Knudsen number.

math.AP↗

arXiv2026

Classical solutions to the Boltzmann equations for gas mixture with unequal molecular masses

The Boltzmann equation is essential for gas thermodynamics,as it models how the molecular density distribution $F(t,x,v)$ changes over time. However, existing research primarily focuses on the single species Boltzmann equation, while investigations into gas mixtures with unequal molecular masses remain relatively limited. Notably, mixed gas studies have broader applications exemplified by Earth's atmosphere, composed of 78\% nitrogen, 21\% oxygen, and 1\% trace gases, where the $N_2$ to $O_2$ molecular mass ratio is 28:32 (simplified as 7:8). This work addresses the Boltzmann equations for such mixtures with unequal molecular masses $(m^A\neq m^B)$, establishing the global in time existence of classical solutions near Maxwellians for soft potentials ($-3<γ<0$) in a periodic spatial domain. Our analysis encompasses arbitrary molecular mass ratios. Our analysis encompasses arbitrary molecular mass ratios. The main contribution of this paper lies in the detailed characterization of the linear collision operator's structure and establishing estimates for the nonlinear terms under unequal mass conditions. Consequently, these results may help advance spectral analysis for soft potentials as well as $L^2,L^{\infty}$ frameworks in future studies of multi-component Boltzmann equations.

math.AP↗

arXiv2026

Hydrodynamic limit of the Vlasov-Poisson-Boltzmann system for gas mixture

In this paper, we study the hydrodynamic limit of the Vlasov-Poisson-Boltzmann system for a gas mixture in the whole space $(x \in \mathbb{R}^3)$ with the potential range of $γ\in\left(-3, 1\right]$. Using the method of Hilbert expansion, we first derive a bi-Maxwellian determined by the Euler-Poisson system of two fluids. To justify the convergence of the solution rigorously as the Knudsen number tends to zero, we sequentially calculate the first $2k-1$ terms of the expansion series $(k \geq 6)$, and then truncate it, and express the solution as the sum of these first $2k-1$ terms and a remainder term. Within the framework of the $L_{x,v}^2-W_{x,v}^{1,\infty}$ interplay established by Guo and Jang \cite{[ininp]Guo2010CMP}, we construct a new weight function to estimate the remainder term in four different cases regarding the potential $γ$. Here, the particle masses $m^A, m^B > 0$ and their charges $e^A, e^B$ can be given arbitrarily. This causes the collision operator to exhibit asymmetric effects ($m^A \neq m^B$), rendering the system of equations impossible to decouple. So, it adds difficulties to both $L^2$, $L^{\infty}$ estimates for the remainder. Therefore, we adopt the framework of vector-valued functions and analyze the velocity decay rate of the operator $K_{M,2,w}^{α,c}$ to eliminate the singularity induced by small parameters in characteristic line iterations. Our results show that the validity time of the solution is $O(\varepsilon^{-y})$, where $y$ is $-\frac{2k-3}{2(2k-1)}$ when $-1 \leq γ\leq 1$, and it becomes $-\frac{2k-3}{(1-γ)(2k-1)}$, when $-3 < γ< -1$. These results possess strong physical realism and can be applied to analyze gas flow dynamics in the daytime ionosphere at high altitudes above the Earth.

math.AP↗