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Zhibing Zhang

Publications and source records attributed to Zhibing Zhang.

14 recordsLinked to original sources
arXiv2026

VERPO: Verified Evidence Regularized Policy Optimization

Verifiable outcome rewards guide language-model post-training, but sequence-level advantages do not identify which token-level decisions should be preserved or revised. Evidence-conditioned Teachers provide denser supervision by replaying sampled trajectories with privileged feedback. Yet indiscriminate imitation risks transferring formatting or reasoning-style shifts that do not support task success. We introduce VERPO, a Verified Evidence Regularized Policy Optimization framework that treats evidence as a proposal for policy correction while retaining the outcome objective. It separates evidence-free reference restoration from signed token-level evidence corrections. Fisher Evidence Contrast attenuates corrections along an estimated evidence-presence direction. A stopped token-wise ZPD controller scales acceptance according to local reward alignment and Fisher movement cost, while the reference channel remains independent of acceptance. Across five scientific-reasoning and tool-use tasks, the best variant on each backbone exceeds the strongest compared baseline in average score. The averages rise from 0.6826 to 0.6857 on Qwen3-4B, from 0.6895 to 0.7058 on Qwen3-8B, and from 0.4751 to 0.5657 on Llama-3.2-1B.

cs.LG↗
arXiv2026

Two improved Liouville-type theorems for the 3D stationary tropical climate model without temperature assumptions

In this paper, we establish two improved Liouville-type theorems for the three-dimensional stationary tropical climate model without imposing any temperature assumptions. Owing to the special structure inherent to the equations, we fully exploit the $L^2$-estimate for the oscillation of the temperature, refined interpolation techniques and an iteration argument to establish a Liouville-type theorem under more flexible and relaxed power-law growth conditions. As an interesting consequence, we obtain the triviality of solutions under the integrability conditions imposed only on $(u,\nabla v)$ or $(\nabla u,\nabla v)$. Furthermore, by developing a systematic framework to handle the energy function associated with the non-trivial solutions and with the aid of delicate ODE analysis and a contradiction argument, we refine our Liouville-type theorem by introducing logarithmic corrections to the growth rates.

math.AP↗
arXiv2025

Some new Liouville type theorems for the 3D stationary magneto-micropolar fluid equations

In this paper, we investigate Liouville type theorems for the 3D stationary magneto-micropolar fluid equations and micropolar fluid equations. Adopting an iteration procedure, taking advantage of the special structure of the equations and using a novel combination of interpolation techniques, we establish Liouville type theorems if the smooth solution satisfies certain growth conditions in terms of $L^p$-norms on the annuli. Furthermore, combining the energy method and some subtle ODE analysis, we relax the growth conditions on the velocity field and the magnetic field by logarithmic factors and obtain logarithmic improvement of Liouville type theorems. Compared with the velocity and the magnetic field, we raise the most relaxed restriction for the angular velocity. More specifically, we allow $L^q$-norm of the angular velocity on the annuli to grow polynomially at any degree, i.e. $\|\omega\|_{L^q(B_{2R}\backslash B_{3R/2})}$ is permitted to grow as fast as $R^N$ at infinity, where $N$ is an arbitrary positive integer.

math.AP↗
arXiv2025

Some remarks on Liouville type theorems for the 3D steady tropical climate model

Observing the special structure of the system and using the Poincar{\'{e}}-Sobolev inequality, we establish Liouville type theorems for the 3D steady tropical climate model under certain conditions on $u$, $v$, $\nabla \theta$. Our results extend and improve a Liouville type result of Cho-In-Yang (arXiv:2312.17441).

math.AP↗
arXiv2025

Some new Liouville type theorems for 3D steady tropical climate model

In this paper, we establish two major classes of Liouville type results for the three-dimensional stationary tropical climate model. The first class is obtained under the assumptions imposed on $u,v,\theta$ whereas the second one relies on the assumptions imposed on $u,v,\nabla\theta$. Using the energy method and an iteration argument, we obtain Liouville type theorems under the condition that Lebesgue norms of the smooth solutions on the annulus satisfy some power-law growth conditions. As a consequence, we show that a smooth solution is trivial provided that it belongs to some Lebesgue spaces or satisfies some decay conditions at infinity. Furthermore, with the aid of a contradiction argument and by developing a systematic framework to handle the energy function associated with the non-trivial solutions, we obtain a logarithmic improvement of our Liouville type theorems. Our new framework is very effective for establishing logarithmic improvements of Liouville type theorems for coupled fluid equations.

math.AP↗
arXiv2025

New Liouville type theorems for 3D steady incompressible MHD equations and Hall-MHD equations

In this paper, we study Liouville type results for the three-dimensional stationary incompressible MHD equations and Hall-MHD equations. Using the energy method and an iteration argument, we establish Liouville type theorems if Lebesgue norms of the velocity and magnetic field on the annulus satisfy certain growth conditions. Furthermore, by establishing new energy estimates and developing some novel differential inequality techniques, we relax the growth conditions by logarithmic factors and obtain logarithmic improvement version of Liouville type theorems. For the MHD equations, the assumptions imposed on the magnetic field are weaker and wider than that of the velocity field in certain sense. Our results extend and improve several recent works.

math.AP↗
arXiv2021

An improved Liouville type theorem for Beltrami flows

In this note, we improved the Liouville type theorem for the Beltrami flows. Two different methods are used to prove it. One is the monotonicity method, and the other is proof by contradiction. The conditions that we proposed on Beltrami flows are significantly weaker than previously known conditions.

math.AP↗
arXiv2019

Existence and Regularity of Weak Solutions for a Thermoelectric Model

This paper concerns a time-independent thermoelectric model with two different boundary conditions. The model is a nonlinear coupled system of the Maxwell equations and an elliptic equation. By analyzing carefully the nonlinear structure of the equations, and with the help of the De Giorgi-Nash estimate for elliptic equations, we obtain existence of weak solutions on Lipschitz domains for general boundary data. Using Campanato's method, we establish regularity results of the weak solutions.

math.AP↗
arXiv2018

Applications of a formula on Beltrami flow

In this note, we obtain uniqueness results for Beltrami flow in both bounded and unbounded domain with nonempty boundary by establishing an elementary but useful formula involving operators $\divg$ and $\curl$. We also use this formula to deal with Maxwell and Stokes eigenvalue problems.

math.AP↗
arXiv2018

Comparison results for eigenvalues of curlcurl operator and Stokes operator

This paper mainly establishes comparison results for eigenvalues of $\curl\curl$ operator and Stokes operator. For three-dimensional simply connected bounded domains, the $k$-th eigenvalue of $\curl\curl$ operator under tangent boundary condition or normal boundary condition is strictly smaller than the $k$-th eigenvalue of Stokes operator. For any dimension $n\geq2$, the first eigenvalue of Stokes operator is strictly larger than the first eigenvalue of Dirichlet Laplacian. For three-dimensional strictly convex domains, the first eigenvalue of $\curl\curl$ operator under tangent boundary condition or normal boundary condition is strictly larger than the second eigenvalue of Neumann Laplacian.

math.AP↗
arXiv2016

Fractional integral operator for $L^1$ vector fields and its applications

This paper studies fractional integral operator for vector fields in weighted $L^1$. Using the estimates on fractional integral operator and Stein-Weiss inequalities, we can give a new proof for a class of Caffarelli-Kohn-Nirenberg inequalities and establish new $\divg$-$\curl$ inequalities for vector fields.

math.CA↗
arXiv2014

Hardy-type inequalities for vector fields with the tangential components vanishing

This note studies the Hardy-type inequalities for vector fields with the $L^1$ norm of the $\curl$. In contrast to the well-known results in the whole space for the divergence-free vectors, we generalize the Hardy-type inequalities to the bounded domains and to the non-divergence-free vector fields with the tangential components on the boundary vanishing.

math.AP↗