arXiv subjects

Shaoheng Zhang

Publications and source records attributed to Shaoheng Zhang.

8 recordsLinked to original sources

arXiv2026

DART-VLN: Test-Time Memory Decay and Anti-Loop Regularization for Discrete Vision-Language Navigation

Memory-based agents for discrete vision-language navigation (VLN) operate under partial observability and may exhibit systematic inference-time failures even with strong pretrained backbones. This paper addresses two recurring problems: stale historical evidence during memory readout and inefficient local backtracking during action selection. We present DART-VLN, a training-free inference-time framework that combines Test-Time Memory Decay, which reweights stale and redundant memory slots without modifying their stored content, with Anti-Loop Regularization, a lightweight next-hop penalty that discourages immediate reversals. DART-VLN introduces no learnable parameters and leaves the navigation backbone unchanged. Experiments on R2R and REVERIE showed that memory decay preserved or improved task performance while reducing runtime. The addition of anti-loop regularization further shortened trajectories, reduced local backtracking, and achieved the best overall balance between navigation quality and efficiency among the evaluated GridMM variants. These results indicate that lightweight inference-time control can improve the reliability and efficiency of memory-based discrete VLN without retraining.

cs.RO↗

arXiv2026

Forced self-similar solutions to the stationary Navier--Stokes equations in a half-space

We study axisymmetric self-similar solutions to the stationary Navier--Stokes equations in the half-space with the no-slip boundary condition, driven by an axisymmetric (-3)-homogeneous external force. If the tangential curl of the force on the unit sphere is sufficiently small, we prove the existence of a unique small solution; when the force is swirl-free, the solution is automatically swirl-free and unique. For a swirl-free external force $\boldsymbol{F}$, we introduce a scaling parameter $λ$ and consider the system with force $λ\boldsymbol{F}$; we prove that solutions exist precisely for $λ$ in an open interval containing zero. The same approach extends to solid cones with the no-slip boundary condition, where narrower opening angles allow the existence of solutions under larger external forces.

math.AP↗

arXiv2026

Asymptotic stability of Landau solutions to the MHD system and energy decay

We consider the three-dimensional incompressible MHD system. Any weak solution satisfying a strong energy inequality is $L^2$-asymptotically stable around a Landau solution. Under an additional integrability assumption on the initial perturbation, we also obtain an explicit algebraic decay rate for the $L^2$-norm of the velocity and magnetic perturbations.

math.AP↗

arXiv2026

On axisymmetric self-similar solutions to the MHD system

Let $(\mathbf{u},\mathbf{B})$ be an axisymmetric self-similar solution to the stationary MHD equations with magnetic diffusion, of the form $\mathbf{u}=u^r(r,z)\mathbf{e}_{r}+u^θ(r,z)\mathbf{e}_θ+u^z(r,z)\mathbf{e}_{z}$ and $\mathbf{B}=B^θ(r,z)\mathbf{e}_θ$ in cylindrical coordinates $(r,θ,z)$, where $(\mathbf{e}_r,\mathbf{e}_θ,\mathbf{e}_z)$ is the orthonormal basis. Under the assumption that $u^r < \frac{1}{3r} + \frac{2r}{3}$ on the unit sphere and on its intersection with the half-space, respectively, we prove two main results. First, for the domain $\mathbb{R}^3\setminus\{0\}$, the velocity field $\mathbf{u}$ must be a Landau solution and the magnetic field $\mathbf{B} \equiv 0$. Second, in the half-space $\mathbb{R}^3_+$ with either the no-slip or Navier slip boundary condition, we establish that all such axisymmetric self-similar solutions are trivial, i.\,e., $\mathbf{u}=\mathbf{B}=0$.

math.AP↗

arXiv2025

Axisymmetric self-similar solutions to the MHD equations without magnetic diffusion

We study the axisymmetric self-similar solutions $(\mathbf{u},\mathbf{B})$ to the stationary MHD equations without magnetic diffusion, where $\mathbf{B}$ has only the swirl component. Our first result states that in $\mathbb{R}^3\setminus\{0\}$, $\mathbf{u}$ is a Landau solution and $\mathbf{B}=0$. Our second result proves the triviality of axisymmetric self-similar solutions in the half-space $\mathbb{R}^3_+$ with the no-slip boundary condition or the Navier slip boundary condition.

math.AP↗

arXiv2025

Point Singularities of Solutions to the Stationary Incompressible MHD Equations

We investigate the point singularity of very weak solutions $(\mathbf{u},\mathbf{B})$ to the stationary MHD equations. More precisely, assume that the solution $(\mathbf{u},\mathbf{B})$ in the punctured ball $B_2\setminus \{0\}$ satisfies the vanishing condition (4), and that $|\mathbf{u}(x)|\le \varepsilon |x|^{-1},\ |\mathbf{B}(x)|\le C |x|^{-1}$ with small $\varepsilon>0$ and general $C>0$. Then, the leading order term of $\mathbf{u}$ is a Landau solution, while the $(-1)$ order term of $\mathbf{B}$ is $0$. In particular, for axisymmetric solutions $(\mathbf{u}, \mathbf{B})$, the condition (4) holds provided $\mathbf{B} = B^θ(r,z) \mathbf{e}_θ$ or the boundary condition (7) is imposed.

math.AP↗

arXiv2024

Lower bounds for the first eigenvalue of the $p$-Laplacian on quaternionic Kähler manifolds

We study the first nonzero eigenvalues for the $p$-Laplacian on quaternionic Kähler manifolds. Our first result is a lower bound for the first nonzero closed (Neumann) eigenvalue of the $p$-Laplacian on compact quaternionic Kähler manifolds. Our second result is a lower bound for the first Dirichlet eigenvalue of the $p$-Laplacian on compact quaternionic Kähler manifolds with smooth boundary. Our results generalize corresponding results for the Laplacian eigenvalues on quaternionic Kähler manifolds proved in [22].

math.DG↗

arXiv2022

Lower bounds for the first eigenvalue of $p$-Laplacian on Kähler manifolds

We study the eigenvalue problem for the $p$-Laplacian on Kähler manifolds. Our first result is a lower bound for the first nonzero eigenvalue of the $p$-Laplacian on compact Kähler manifolds in terms of dimension, diameter, and lower bounds of holomorphic sectional curvature and orthogonal Ricci curvature for $p\in (1, 2]$. Our second result is a sharp lower bound for the first Dirichlet eigenvalue of the $p$-Laplacian on compact Kähler manifolds with smooth boundary for $p\in (1, \infty)$. Our results generalize corresponding results for the Laplace eigenvalues on Kähler manifolds proved in [14].

math.DG↗