arXiv subjects

Mingxue Zhang

Publications and source records attributed to Mingxue Zhang.

5 recordsLinked to original sources

arXiv2026

Blow-up at arbitrary energy levels for a strongly damped viscoelastic wave equation with a variable-exponent logarithmic source

We study a strongly damped viscoelastic wave equation with a logarithmic source whose measurable exponent satisfies $2<p_-\le p(x) \le p_+<2^*$. An optimal pointwise correction to the source--potential inequality defines a \emph{shifted energy}. Under suitable kernel conditions, we prove finite-time blow-up for negative shifted energy and for a class of nonnegative shifted energies with no fixed upper energy threshold. Explicit upper lifespan bounds follow from an estimate for reaching negative shifted energy and a concavity argument. We also construct smooth blow-up data at every prescribed real energy level and show that our lifespan estimate covers additional data in the constant-exponent case. Explicit examples are given to illustrate the blow-up results.

math.AP↗

arXiv2026

Linear ill-posedness of three-dimensional MHD boundary layer equations

We prove linear ill-posedness in tangential Sobolev spaces for the three-dimensional resistive MHD boundary layer equations. We assume that a suitable linear combination of the initial tangential velocity components has a non-degenerate critical point and that both initial tangential magnetic components have a double zero at the same point. Compared with the corresponding two-dimensional MHD result, our construction requires only this double-zero condition, rather than a higher-order degeneracy of the magnetic shear. The proof combines the three-dimensional Prandtl critical layer construction with a vector correction to the two-dimensional magnetic quotient. This correction cancels the leading terms in both induction equations while preserving the magnetic divergence constraint. The resulting approximate solutions grow like $\exp(σt/\sqrt{\varepsilon})$, and their residuals have a prefactor of order $O(\varepsilon^{-3/8})$, up to logarithmic factors. A Duhamel argument then yields linear ill-posedness for every tangential derivative loss $μ<\frac18$. Thus the three-dimensional Prandtl instability persists when the stabilizing tangential magnetic field degenerates.

math.AP↗

arXiv2026

Local Well-Posedness of the Boundary Layer Equations for Dilatant Power-Law Fluids

We establish the local-in-time existence and uniqueness of monotone solutions to the two-dimensional nonstationary boundary-layer equations for a dilatant power-law fluid in a periodic half-space for $1<n<\frac{7}{3}$. Under Oleinik's monotonicity condition and suitable weighted Sobolev assumptions on the initial data and outer flow, we construct solutions through tangential regularization and derive uniform a priori estimates. A suitable good unknown compensates for the loss of one tangential derivative caused by the normal velocity. By combining weighted energy estimates, the Faà di Bruno formula, and the maximum and minimum principles, we control the nonlinear degenerate diffusion term $\partial_y^2(ω^n)$, whose effective diffusion coefficient vanishes as $ω=\partial_yu$ decays at infinity, and propagate the weighted monotonicity of the vorticity. Within this exponent range, our result partially resolves the eleventh open problem posed by Oleinik and Samokhin \cite{OAO} on the existence and uniqueness of solutions to nonstationary boundary-layer systems for dilatant fluids.

math.AP↗

arXiv2025

Explainer-guided Targeted Adversarial Attacks against Binary Code Similarity Detection Models

Binary code similarity detection (BCSD) serves as a fundamental technique for various software engineering tasks, e.g., vulnerability detection and classification. Attacks against such models have therefore drawn extensive attention, aiming at misleading the models to generate erroneous predictions. Prior works have explored various approaches to generating semantic-preserving variants, i.e., adversarial samples, to evaluate the robustness of the models against adversarial attacks. However, they have mainly relied on heuristic criteria or iterative greedy algorithms to locate salient code influencing the model output, failing to operate on a solid theoretical basis. Moreover, when processing programs with high complexities, such attacks tend to be time-consuming. In this work, we propose a novel optimization for adversarial attacks against BCSD models. In particular, we aim to improve the attacks in a challenging scenario, where the attack goal is to limit the model predictions to a specific range, i.e., the targeted attacks. Our attack leverages the superior capability of black-box, model-agnostic explainers in interpreting the model decision boundaries, thereby pinpointing the critical code snippet to apply semantic-preserving perturbations. The evaluation results demonstrate that compared with the state-of-the-art attacks, the proposed attacks achieve higher attack success rate in almost all scenarios, while also improving the efficiency and transferability. Our real-world case studies on vulnerability detection and classification further demonstrate the security implications of our attacks, highlighting the urgent need to further enhance the robustness of existing BCSD models.

cs.CR↗

arXiv2020

The unique global solvability of the nonhomogeneous incompressible asymmetric fluids with vacuum

The present paper deals with the nonhomogeneous incompressible asymmetric fluids equations in dimension $d= 2,3$. The aim is to prove the unique global solvability of the system with only bounded nonnegative initial density and $H^{1}$ initial velocities. We first construct the global existence of the solution with large data in 2-D. Next, we establish the existence of local in time solution for arbitrary large data and global in time for some smallness conditions in 3-D. Finally, the uniqueness of the solution is proved under quite soft assumptions about its regularity through a Lagrangian approach. In particular, the initial vacuum is allowed.

math.AP↗