Related papers: Global existence and minimal decay regularity for …
This work first gives the global existence and optimal decay rates of solutions to the classical Timoshenko system on the framework of Besov spaces. Due to the \textit{non-symmetric} dissipation, the general theory for dissipative…
Dissipative hyperbolic systems of \textit{regularity-loss} have been recently received increasing attention. Usually, extra higher regularity is assumed to obtain the optimal decay estimates, in comparison with that for the global-in-time…
In this paper, we are concerned with the convergence rates of the global strong solution to constant equilibrium state for the compressible viscoelastic fluids in the whole space. We combine both analysis about Green's matrix method and…
In this paper, we study the large time behavior of solutions to the compressible magnetohydrodynamic equations in the $L^p$-type critical Besov spaces. Precisely, we show that if the initial data in the low frequencies additionally belong…
Danchin and He (Math. Ann. 64: 1-38, 2016) recently established the global existence in critical $L^p$-type regularity framework for the $N$-dimensional $(N\geq 3)$ non-isentropic compressible Navier-Stokes equations. The purpose of this…
The present paper is the continuation of work \cite{XC}, devoted to extending it to a critical functional framework which is not related to the energy space. Employing the special dissipative structure of the non-conservative viscous…
Very recently, a new decay framework has been given by [51] for linearized dissipative hyperbolic systems satisfying the Kawashima-Shizuta condition on the framework of Besov spaces, which allows to pay less attention on the traditional…
We give a new decay framework for general dissipative hyperbolic system and hyperbolic-parabolic composite system, which allow us to pay less attention on the traditional spectral analysis in comparison with previous efforts. New…
The global existence issue for the isentropic compressible Navier-Stokes equations in the critical regularity framework has been addressed in [7] more than fifteen years ago. However, whether (optimal) time-decay rates could be shown in…
In this paper, we study large time behavior for the dissipative Timoshenko system in the whole space $\mathbb{R}$, particularly, on the transversal displacement $w$ and the rotation angle $\psi$ of the filament for the beam. Different from…
The compressible Navier-Stokes-Poisson system takes the form of usual Navier-Stokes equations coupled with the self-consistent Poisson equation, which is used to simulate the transport of charged particles under the electric field of…
This paper is concerned with the global stability of non-critical/critical traveling waves with oscillations for time-delayed nonlocal dispersion equations. We first theoretically prove that all traveling waves, especially the critical…
In this paper, we investigate the decay properties of the thermoelastic Timoshenko system with past history in the whole space where the thermal effects are given by Cattaneo and Fourier laws. We obtain that both systems, Timoshenko-Fourier…
This paper investigates the Cauchy problem for the compressible pressureless Navier-Stokes system in $\mathbb{R}^d$ with $d \geq 2$. Unlike the standard isentropic compressible Navier-Stokes system, the density in the pressureless model…
This paper concerns the global-in-time evolution of a generic compressible two-fluid model in $\mathbb{R}^d$ ($d\geq3$) with the common pressure law. Due to the non-dissipative properties for densities and two different particle paths…
In this paper, we consider the Cauchy problem of a model in nonlinear acoustic, named the Jordan--Moore--Gibson--Thompson equation. This equation arises as an alternative model to the well-known Kuznetsov equation in acoustics. We prove…
Due to the dissipative structure of \textit{regularity-loss}, extra higher regularity than that for the global-in-time existence is usually imposed to obtain the optimal decay rates of classical solutions to dissipative systems. The aim of…
In this paper, we consider the following dissipative viscoelastic with memory-type Timoshenko system \begin{equation*} \begin{gathered} \begin{cases} \rho_1 \phi_{tt} - \kappa ( \phi _{x} + \psi) _x + \kappa \int_0^\infty g(s) (\phi_x…
We consider the large time behavior of global strong solutions to the compressible viscoelastic flows on the whole space $\mathbb{R}^N\,(N\geq 2)$, where the system describes the elastic properties of the compressible fluid. Adding a…
A paper, entitled "Uniform stabilization for the Timoshenko beam by a locally distributed damping" was published in 2003, in the journal Electronic Journal of Differential Equations. Its title concerns exclusively its Section 3, devoted to…