arXiv subjects

Bingqi Yu

Publications and source records attributed to Bingqi Yu.

3 recordsLinked to original sources

arXiv2026

Effective stability for Hamiltonian PDEs vanishing spectral gaps

This paper studies the effective stability of nearly integrable Hamiltonian PDEs with asymptotically vanishing spectral gaps ($0 < \alpha < 1$). Under a unified high-low frequency decomposition, we construct a modified block clustering partition based on Bourgain's ideas. By leveraging the vanishing of spectral gaps to suppress high-frequency resonant contributions, the overall non-resonance property is maintained under high-regularity weights. This framework is applied to space fractional and fully dispersive Whitham-Schr\"odinger equations, uniformly yielding explicit stability estimates in Gevrey, logarithmic ultra-differentiable, and Sobolev spaces.

math.AP↗

arXiv2025

Nekhoroshev type stability for non-local semilinear Schr\"odinger equations

This paper investigates Nekhoroshev-type stability for solutions of ultra-differentiable regularity in Schr\"odinger equations with non-local nonlinear terms, employing the method of rational normal forms. We establish the first rigorous results for logarithmic ultra-differentiable regularity in infinite-dimensional Hamiltonian systems without external parameters. Under Gevrey class regularity assumptions, we achieve the stability times matching Bourgain's conjectured optimal stability time in \cite{B04}. Furthermore, we introduce a novel global vector field norm adapted to the rational normal form framework. This norm eliminate the need for degree tracking during the iteration process, thereby enabling a unified treatment of nonlinear terms.

math.AP↗

arXiv2025

Almost global existence for Ultra-differential Hamiltonian in $L^2$ space

This paper combines the decay of high modes with the smallness introduced by high orders, leading to a normal form lemma for infinite-dimensional Hamiltonian systems under ultra-differentiable regularity. We prove the sub-exponential stability time of a wide class of Hamiltonian PDEs, including the Schr\"odinger equation with convolution potentials, fractional-order Schr\"odinger equations, and beam equations with metrics. When the conditions are equivalent to previous ones, the stability time we obtain reaches Bourgain's predicted optimal bound. Furthermore, we approach earlier results under lower conditions. These results are discussed within a general framework we propose, which applies to the ultra-differential class.

math.AP↗