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Guoquan Qin

Publications and source records attributed to Guoquan Qin.

7 recordsLinked to original sources
arXiv2021

Orbital stability of peakon solutions for a generalized higher-order Camassa-Holm equation

In this paper, we investigate the orbital stability issue of a generalized higher-order Camassa-Holm (HOCH) equation, which is an higher-order extension of the quadratic CH equation. Firstly, we show that the HOCH equation admits a global weak peakon solution by paring it with ssome smooth test function. Secondly, with the help of two conserved quantities and the non-sgn-changing condition, we prove the orbital stability of this peakon solution in the energy space in the sense that its shape remains approximately the same for all times. Our results enrich the research of the orbital stability for the CH-type equations and are useful to better understand the impact of higher-order nonlinearities on the dispersion dynamics.

math.AP↗
arXiv2021

The Cauchy problem and wave-breaking phenomenon for a generalized sine-type FORQ/mCH equation

In this paper, we are concerned with the Cauchy problem and wave-breaking phenomenon for a sine-type modified Camassa-Holm (alias sine-FORQ/mCH) equation. Employing the transport equations theory and the Littlewood-Paley theory, we first establish the local well-posedness for the strong solutions of the sine-FORQ/mCH equation in Besov spaces. In light of the Moser-type estimates, we are able to derive the blow-up criterion and the precise blow-up quantity of this equation in Sobolev spaces. We then give a sufficient condition with respect to the initial data to ensure the occurance of the wave-breaking phenomenon by trace the precise blow-up quantity along the characteristics associated with this equation.

math.AP↗
arXiv2019

Existence and stability of periodic solution to the 3D Ginzburg-Landau equation in weighted Sobolev spaces

We prove the existence of time periodic solution to the 3D Ginzburg-Landau equation in weighted Sobolev spaces. We consider the cubic Ginzburg-Landau equation with an external force $g$ satisfying the oddness condition $g(-x,t)=-g(x,t)$. The existence of the periodic solution is proved for small time-periodic external force. The stability of the time periodic solution is also considered.

math.AP↗
arXiv2019

Navier-Stokes equations with external forces in Besov-Morrey spaces

We establish the existence and uniqueness of local strong solutions to the Navier-Stokes equations with arbitrary initial data and external forces in the homogeneous Besov-Morrey space. The local solutions can be extended globally in time provided the initial data and external forces are small. We adapt the method introduced in \cite{ks6}, where the Besov space is considered, to the setting of the homogeneous Besov-Morrey space.

math.AP↗
arXiv2018

On the propagation of regularity and decay of solutions to the Benjamin equation

In this paper, we investigate some special regularities and decay properties of solutions to the initial value problem(IVP) of the Benjamin equation. The main result shows that: for initial datum $u_{0}\in H^{s}(\mathbb{R})$ with $s>3/4,$ if the restriction of $u_{0}$ belongs to $H^{l}((x_{0}, \infty))$ for some $l\in \mathbb{Z}^{+}$ and $x_{0}\in \mathbb{R},$ then the restriction of the corresponding solution $u(\cdot, t)$ belongs to $H^{l}((α, \infty))$ for any $α\in \mathbb{R}$ and any $t\in(0, T)$. Consequently, this type of regularity travels with infinite speed to its left as time evolves.

math.AP↗