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Generically sharp decay and blowing up at infinity for a weak null wave system
Shijie Dong, Siyuan Ma, Yue Ma +1
We study a system of semilinear wave equations satisfying the weak null condition, which can be regarded as a simplified model for the Einstein vacuum equations. The main objective…
Quantitative observability for one-dimensional Schrödinger equations with potentials
Pei Su, Chenmin Sun, Xu Yuan
In this note, we prove the quantitative observability with an explicit control cost for the 1D Schrödinger equation over with real-valued, bounded continuous potentia…
Global Behavior of Small Data Solutions for The 2D Dirac-Klein-Gordon Equations
Shijie Dong, Kuijie Li, Yue Ma +1
In this paper, we are interested in the two-dimensional Dirac-Klein-Gordon system, which is a basic model in particle physics. We investigate the global behaviors of small data sol…
Asymptotic behavior of 2D Wave-Klein-Gordon coupled system under null condition
Shijie Dong, Yue Ma, Xu Yuan
We study the 2D coupled wave-Klein-Gordon systems with semi-linear null nonlinearities and . The main result states that the solution to the 2D coupled systems exists…
Construction of excited multi-solitons for the focusing 4D cubic wave equation
Xu Yuan
Consider the focusing 4D cubic wave equation \[ \partial_{tt}u-Δu-u^{3}=0,\quad \mbox{on}\ (t,x)\in [0,\infty)\times \mathbb{R}^{4}.\] The main result states the existence in energ…
Asymptotics of solutions with a compactness property for the nonlinear damped Klein-Gordon equation
Raphaël Côte, Xu Yuan
We consider the nonlinear damped Klein-Gordon equation \[ \partial_{tt}u+2α\partial_{t}u-Δu+u-|u|^{p-1}u=0 \quad \text{on} \ \ [0,\infty)\times \mathbb{R}^N \] with , $2 \le N…