arXiv subjects

Jiayan Wu

Publications and source records attributed to Jiayan Wu.

7 recordsLinked to original sources

arXiv2026

Nonexistence Results and Constructions for Signed Difference Sets

Signed difference sets (SDSs) extend ordinary difference sets by allowing negative coefficients. We establish new nonexistence criteria and existence constructions for SDSs in finite abelian groups. Using the classical self-conjugate-prime method and a support-refined quotient method, we derive four obstructions, including the $C_2$-quotient, near-full-support, and small-defect obstructions. Applied cumulatively to the $67{,}823$ open group-specific cases in the database with $9\leq v\leq499$, these criteria rule out $45{,}361$ cases. For existence, we construct an infinite family from PCP-type regular partial difference sets arising from Desarguesian spreads and an explicit $(125,28,3)$-SDS in $C_5^3$ using quartic multiplicative characters. These constructions settle three further open cases.

math.CO↗

arXiv2026

Robust Observability for Schr\"odinger Equations with Rough Potentials on 2D Compact Hyperbolic Surfaces

This paper investigates the robustness of quantum observability on compact hyperbolic surfaces under $L^2$ potential perturbations. Since $L^2$ regularity is strictly subcritical in dimension two, for every non-empty open set $\Omega\subset M$ and $T>0$, the solution of $(i\partial_t+\Delta-V)u=0$ satisfies the space-time observability estimate $$ \|u_0\|_{L^2(M)}^2 \leq C\int_0^T \|e^{-it(-\Delta+V)}u_0\|_{L^2(\Omega)}^2\,dt. $$ Our results provide a quantitative confirmation that the delocalization of high-energy quantum states on negatively curved manifolds is robust against $L^2$-class microscopic scattering. The proof combines the hyperbolic dynamics of the geodesic flow with semiclassical analysis. A key ingredient is an $L^4$ spectral cluster estimate with an arbitrarily small loss, obtained by exploiting Jacobi field analysis and Bourgain--Demeter $l^2$-decoupling. This estimate allows us to obtain refined spectral localized semiclassical Strichartz estimates adapted to rough potentials and to show that the potential's contribution vanishes in the propagation of semiclassical measures. The full-support property of invariant semiclassical measures on hyperbolic surfaces then yields the desired observability by contradiction. By the Hilbert Uniqueness Method, the corresponding internal controllability result follows.

math.AP↗

arXiv2026

Local decay estimates for the bi-Laplacian Nonautonomous Schr\"{o}dinger equation

In this paper, we establish local decay estimates for the bi-Laplacian Schr\"{o}dinger equation with time-dependent (in particular, quasi-periodic) potentials in spatial dimension $n\ge14$. Moreover, under stronger spectral regularity hypotheses, the same result can be extended to dimension $n\ge9$. Our approach, based on asymptotic completeness and the existence of the channel wave operator, departs from standard resolvent-based methods. In addition, global-in-time Strichartz estimates are derived from the local decay estimates.

math.AP↗

arXiv2025

High-capillarity limit and smoothing effect of large solutions for a multi-dimensional generic non-conservative compressible two-fluid model

We investigate the global existence and long-time behavior of large solutions, in the high-capillarity regime, for a general multidimensional non-conservative compressible two-fluid model with the capillary pressure relation $f(\alpha^{-}\rho^{-})=P^{+}-P^{-}$. Our main contributions are threefold. First, for sufficiently large capillarity coefficients, we prove the existence and uniqueness of global solutions in critical Besov spaces for large initial perturbations, under the sharp stability condition $-\frac{s_{-}^{2}(1,1)}{\alpha^{-}(1,1)}<f^{\prime}(1)<0$, thereby removing the additional negativity restriction assumed by Evje--Wang--Wen [Arch. Ration. Mech. Anal. 221:1285--1316, 2016]. Second, we give a rigorous justification of the global-in-time convergence to the incompressible Navier-Stokes flows and obtain explicit convergence rates in critical spaces for ill-prepared data. Third, if in addition the initial perturbation lies in a lower-regularity Besov space, we derive optimal decay rates for the solution and for its derivatives of any order, revealing a long-term smoothing effect. To the best of our knowledge, this is the first result on global large-amplitude strong solutions for multidimensional compressible two-fluid flows. Our analysis exploits the interplay between dispersion (two-phase Gross--Pitaevskii structure) and parabolic dissipation, both induced by capillarity effects.

math.AP↗

arXiv2025

The non-conservative compressible two-fluid system with common pressure: Global existence and sharp time asymptotics

This paper concerns the global-in-time evolution of a generic compressible two-fluid model in $\mathbb{R}^d$ ($d\geq3$) with the common pressure law. Due to the non-dissipative properties for densities and two different particle paths caused by velocities, the system lacks the usual symmetry structure and is partially dissipative in the sense that the Shizuta-Kawashima condition is violated, which makes it challenging to study its large-time stability. By developing a pure energy method in the framework of Besov spaces, we succeed in constructing a unique global classical solution to the Cauchy problem when the initial data are close to their constant equilibria. Compared to the previous related works, the main novelty lies in that our method is independent of the spectral analysis and does not rely on the $L^1$ smallness of the initial data. Furthermore, if additionally the initial perturbation is bounded in $\dot{B}^{\sigma_0}_{2,\infty}$ type spaces with lower regularity, the optimal time convergence rates are also obtained. In particular, the asymptotic convergence of the non-dissipative components toward their equilibrium states is first characterized.

math.AP↗

arXiv2024

RIS-Based Self-Interference Cancellation for Full-Duplex Broadband Transmission

Full-duplex (FD) is an attractive technology that can significantly boost the throughput of wireless communications. However, it is limited by the severe self-interference (SI) from the transmitter to the local receiver. In this paper, we propose a new SI cancellation (SIC) scheme based on reconfigurable intelligent surface (RIS), where small RISs are deployed inside FD devices to enhance SIC capability and system capacity under frequencyselective fading channels. The novel scheme can not only address the challenges associated with SIC but also improve the overall performance. We first analyze the near-field behavior of the RIS and then formulate an optimization problem to maximize the SIC capability by controlling the reflection coefficients (RCs) of the RIS and allocating the transmit power of the device. The problem is solved with alternate optimization (AO) algorithm in three cases: ideal case, where both the amplitude and phase of each RIS unit cell can be controlled independently and continuously, continuous phases, where the phase of each RIS unit cell can be controlled independently, while the amplitude is fixed to one, and discrete phases, where the RC of each RIS unit cell can only take discrete values and these discrete values are equally spaced on the unit circle. For the ideal case, the closed-form solution to RC is derived with Karush-Kuhn-Tucker (KKT) conditions. Based on Riemannian conjugate gradient (RCG) algorithm, we optimize the RC for the case of continuous phases and then extend the solution to the case of discrete phases by the nearest point projection (NPP) method. Simulation results are given to validate the performance of our proposed SIC scheme.

eess.SP↗

arXiv2023

Decomposition of global solutions of bi-laplacian Nonautonomous Schr\"odinger equations

We study the bi-Laplacian Schr\"odinger equation with a general interaction term, which may be linear or nonlinear and is allowed to be time-dependent. We show that global solutions to such equations decompose asymptotically into a free wave and a weakly localized component in all space dimensions. Moreover, in dimensions $n \geq 9$, we prove that the weakly localized component is in fact spatially localized. The proof is based on a suitably adapted construction of the Free Channel Wave Operator, building on the method recently developed in~\cite{SW20221}.

math.AP↗