In this paper, we investigate the stabilization of a one-dimensional piezoelectric (Stretching
system) with partial viscous dampings. First, by using Lorenz gauge conditions, we …

We make use of Friedrich's representation of spatial infinity to study asymptotic expansions
of the Maxwell-scalar field system near spatial infinity. The main objective of this analysis is …

Hysteresis is highly undesired for the vibration control of piezoelectric beams especially in
high-precision applications. Current-controlled piezoelectric beams cope with hysteresis …

Global well-posedness for the Yang-Mills equation in 4+1 dimensions. Small energy Page 1
Annals of Mathematics 185 (2017), 831–893 https://doi.org/10.4007/annals.2017.185.3.3 …

We prove global regularity, scattering and a priori bounds for the energy critical Maxwell-
Klein-Gordon equation relative to the Coulomb gauge on (1+ 4)(1+ 4)-dimensional …

This article constitutes the final and main part of a three-paper sequence (Ann PDE, 2016.
doi: 10.1007/s40818-016-0006-4; Oh and Tataru, 2015. arXiv: 1503.01561), whose goal is …

We demonstrate null structure in the Yang–Mills equations in Lorenz gauge. Such structure
was found in Coulomb gauge by Klainerman and Machedon, who used it to prove global …

This paper is the first part of a trilogy 22, 23 dedicated to a proof of global well-posedness
and scattering of the (4+ 1)(4+ 1)-dimensional mass-less Maxwell–Klein–Gordon equation …

We first introduce a new model for a two-dimensional gauge-covariant wave equation with
space-time white noise. In our main theorem, we obtain the probabilistic global well …

We prove that the Yang–Mills equations in the Lorenz gauge (YM-LG) is locally well-posed
for data below the energy norm, in particular, we can take data for the gauge potential A and …