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pro vyhledávání: '"Chen, Qionglei"'
We focus on the bilinear Strichartz estimates for free solutions to the Schr\"odinger equation on rescaled waveguides $\mathbb{R} \times \mathbb{T}_\lambda^n$, $\mathbb{T}_\lambda^n=(\lambda\mathbb{T})^n$ with $n\geq 1$ and their applications. First,
Externí odkaz:
http://arxiv.org/abs/2411.10012
Publikováno v:
Journal of Functional Analysis, 286(2024)110302
In this paper, we prove a sharp ill-posedness result for the incompressible non-resistive MHD equations. In any dimension $d\ge 2$, we show the ill-posedness of the non-resistive MHD equations in $H^{\frac{d}{2}-1}(\mathbb{R}^d)\times H^{\frac{d}{2}}
Externí odkaz:
http://arxiv.org/abs/2404.14825
Autor:
Chen, Qionglei, Zhao, Zhiwen
A high-contrast two-phase nonlinear composite material with adjacent inclusions of $m$-convex shapes is considered for $m>2$. The mathematical formulation consists of the insulated conductivity problem with $p$-Laplace operator in $\mathbb{R}^{d}$ fo
Externí odkaz:
http://arxiv.org/abs/2306.03519
Autor:
Chen, Qionglei, Nie, Yao
We study the Cauchy problem of the 2D viscous shallow water equations in some critical Besov spaces $\dot B^{\frac{2}{p}}_{p,1}(\mathbb{R}^2)\times \dot B^{\frac{2}{p}-1}_{p,q}(\mathbb{R}^2)$. As is known, this system is locally well-posed for large
Externí odkaz:
http://arxiv.org/abs/2203.00309
Autor:
Chen, Qionglei, Li, Zhen
Publikováno v:
In Journal of Differential Equations 25 March 2024 386:404-434
Autor:
Chen, Qionglei, Nie, Yao
Publikováno v:
In Journal of Differential Equations 15 December 2023 376:71-101
Autor:
Chen, Qionglei, Zhang, Qi
Publikováno v:
In Applied Mathematics Letters December 2023 146
The paper investigates the existence of global attractors and their upper semicontinuity for a structural damped wave equation on $\mathbb{R}^{N}: u_{tt}-\Delta u+(-\Delta)^\alpha u_{t}+u_{t}+u+g(u)=f(x)$, where $\alpha\in (1/2, 1)$ is called a dissi
Externí odkaz:
http://arxiv.org/abs/1905.06778
Autor:
Chen, Qionglei, Hao, Xiaonan
We prove the global well-posedness in the critical Besov spaces for the incompressible Oldroyd-B model without damping mechanism on the stress tensor in $\mathbb{R}^d$ for the small initial data. Our proof is based on the observation that the behavio
Externí odkaz:
http://arxiv.org/abs/1810.06171
Autor:
Chen, Qionglei, Li, Zhen
Publikováno v:
In Applied Mathematics Letters October 2022 132