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Jingya Zhao

Publications and source records attributed to Jingya Zhao.

6 recordsLinked to original sources

Global dynamics of a supercritical wave equation in a large data regime

We prove the existence of global solutions to the nonlinear wave equation in $\mathbb{R}^{1+3}$ $$\Phi_{tt} - \Delta \Phi \pm \Phi|\Phi|^{p-1} = 0$$ in the energy-supercritical regime $p>5$, for a class of large initial data. Our initial data can be decomposed into two pieces, one which is dispersed in the sense of having large $L^2$ norm, while the other piece takes a localised short-pulse form. Consequently, we can obtain global existence for a class of initial data which is large in every homogeneous Sobolev norm $\dot{H}^s_x$ with $s \geq 0$.

math.AP

Uniform boundedness of conformal energy for the 3D nonlinear wave equation

In this paper, we study three-dimensional nonlinear wave equations under the null condition, a fundamental model in the theory of nonlinear wave-type equations, initially investigated by Christodoulou \cite{Christodoulou86} and Klainerman \cite{Klainerman86}. For a class of large initial data, we establish global existence and linear scattering of solutions by combining refined energy estimates with a bootstrap argument. Moreover, we prove that the lower-order conformal energy remains uniformly bounded for all time.

math.AP

Towards reliable respiratory disease diagnosis based on cough sounds and vision transformers

Recent advancements in deep learning techniques have sparked performance boosts in various real-world applications including disease diagnosis based on multi-modal medical data. Cough sound data-based respiratory disease (e.g., COVID-19 and Chronic Obstructive Pulmonary Disease) diagnosis has also attracted much attention. However, existing works usually utilise traditional machine learning or deep models of moderate scales. On the other hand, the developed approaches are trained and evaluated on small-scale data due to the difficulty of curating and annotating clinical data on scale. To address these issues in prior works, we create a unified framework to evaluate various deep models from lightweight Convolutional Neural Networks (e.g., ResNet18) to modern vision transformers and compare their performance in respiratory disease classification. Based on the observations from such an extensive empirical study, we propose a novel approach to cough-based disease classification based on both self-supervised and supervised learning on a large-scale cough data set. Experimental results demonstrate our proposed approach outperforms prior arts consistently on two benchmark datasets for COVID-19 diagnosis and a proprietary dataset for COPD/non-COPD classification with an AUROC of 92.5%.

cs.CV

Uniform-in-mass global existence for 4D Dirac-Klein-Gordon equations

We are interested in four-dimensional Dirac-Klein-Gordon equations, a fundamental model in particle physics. The main goal of this paper is to establish global existence of solutions to the coupled system and to explore their long-time behavior. The results are valid uniformly for mass parameters varying in the interval $[0,1]$.

math.AP

Large data global existence for coupled massive-massless wave-type systems

We consider 3D Klein-Gordon-Zakharov (KGZ) and Dirac-Klein-Gordon (DKG) systems, where a common feature is that there exist both massless and massive fields in each system. We establish global existence and asymptotic behavior for both systems with a class of large data. More precisely, in the KGZ system, we allow the massless field to be large, while in the DKG system we allow the massive field to be large.

math.AP

Cubic Dirac equations with a class of large data

We are interested in massless cubic Dirac equations in two and three space dimensions, known as the Soler model. The solution to this model is known as a wave function, which has the unit $L^2$ norm. We aim to show global existence and asymptotic behavior for the cubic Dirac model with a class of initial data that can be large in $L^2$.

math.AP