arXiv subjects

Chunxia Guan

Publications and source records attributed to Chunxia Guan.

3 recordsLinked to original sources

arXiv2026

Global dynamics and asymptotic stability for a nonlocal LANS-$α$-type system

This paper is devoted to the global dynamics of a nonlocal Lagrangian-averaged Navier-Stokes-$α$ (LANS-$α$)-type system (also known as the viscous Euler-Poincaré system) in one, two, and three spatial dimensions. In the unforced periodic setting with zero mean, we establish global well-posedness for the initial-value problem and prove that the corresponding solution semigroup is dissipative and possesses a compact global attractor consisting of the singleton $\{0\}$. Furthermore, we obtain the following global-in-time algebraic asymptotic stability estimate: \[ \|u(t,\cdot)\|_{H^3}\lesssim t^{-1/2},\qquad \forall\, t>0, \] which is derived from higher-order energy inequalities combined with a uniform Gronwall-type argument. Our results provide a complete description of the long-time behavior of the unforced periodic dynamics for this nonlocal LANS-$α$-type system.

math.AP↗

arXiv2017

The existence of the global entropy weak solutions for a generalized Camassa-Holm equation

In this paper, we prove the existence of a global entropy weak solution $u\in H^1(\mathbb{R})$ and $\partial_{x}u\in L^1(\mathbb{R})\cap BV(\mathbb{R})$ for the Cauchy problem of a generalized Camassa-Holm equation by the viscous approximation method.

math.AP↗

arXiv2015

Lipschitz metric for the modified two-component Camassa-Holm system

This paper is devoted to the existence and Lipschitz continuity of global conservative weak solutions in time for the modified two-component Camassa-Holm system on the real line. We obtain the global weak solutions via a coordinate transformation into the Lagrangian coordinates. The key ingredients in our analysis are the energy density given by the positive Radon measure and the proposed new distance functions as well.

math.AP↗