arXiv subjects

Yamin Xiao

Publications and source records attributed to Yamin Xiao.

4 recordsLinked to original sources

arXiv2025

Orbital stability of solitary waves for the Schr odinger-Boussinesq system

This paper studies the orbital stability of solitary waves for the following Schrödinger-Boussinesq system \begin{equation*} \begin{cases} { \begin{array}{ll} i\varepsilon_t+\varepsilon_{xx}=n\varepsilon+γ|\varepsilon|^2\varepsilon, \\ n_{tt}-n_{xx}+ αn_{xxxx}-β(n^2)_{xx}=|\varepsilon|^2_{xx}, \end{array} } (t,x)\in \mathbb{R}^2. \end{cases} \end{equation*} By applying the abstract results and detailed spectral analysis, we obtain the orbital stability of solitary waves. The result can be regarded as an extension of the results of \cite{ F-P,H,W}.

math.AP↗

arXiv2024

Prevention of Infinite-time Blowup by Slightly Super-linear Degradation in a Keller--Segel System with Density-suppressed Motility

An initial-Neumann boundary value problem for a Keller--Segel system with density-suppressed motility and source terms is considered. Infinite-time blowup of the classical solution was previously observed for its source-free version when dimension $N\geq2$. In this work, we prove that with any source term involving a slightly super-linear degradation effect on the density, of a growth order of $s\log s$ at most, the classical solution is uniformly-in-time bounded when $N\leq3$, thus preventing the infinite-time explosion detected in the source-free counter-part. The cornerstone of our proof lies in an improved comparison argument and a construction of an entropy inequality.

math.AP↗

arXiv2023

Global Existence and Uniform Boundedness in a Fully Parabolic Keller-Segel System with Non-monotonic Signal-dependent Motility

This paper is concerned with global solvability of a fully parabolic system of Keller--Segel-type involving non-monotonic signal-dependent motility. First, we prove global existence of classical solutions to our problem with generic positive motility function under a certain smallness assumption at infinity, which however permits the motility function to be arbitrarily large within a finite region. Then uniform-in-time boundedness of classical solutions is established whenever the motility function has strictly positive lower and upper bounds in any dimension $N\geq1$, or decays at a certain slow rate at infinity for $N\geq2$. Our results remove the crucial non-increasing requirement on the motility function in some recent work \cite{JLZ22,FJ19b,FS22} and hence allow for both chemo-attractive and chemo-repulsive effect, or their co-existence in applications. The key ingredient of our proof lies in an important improvement of the comparison method developed in \cite{JLZ22,FJ19b,LJ21}.

math.AP↗

arXiv2020

The global well-posedness of strong solutions to 2D MHD equations in Lei-Lin space

In this paper, we study the Cauchy problem of the 2D incompressible magnetohydrodynamic equations in Lei-Lin space. The global well-posedness of a strong solution in the Lei-Lin space $χ^{-1}(\mathbb{R}^2)$ with any initial data in $χ^{-1}(\mathbb{R}^2)\cap L^2(\mathbb{R}^2)$ is established. Furthermore, the uniqueness of the strong solution in $χ^{-1}(\mathbb{R}^2)$ and the Leray-Hopf weak solution in $L^2(\mathbb{R}^2)$ is proved.

math.AP↗