相关论文: Optimal decay rates of the compressible Euler equa…
In this paper, vacuum and singularity formation are considered for compressible Euler equations with time-dependent damping. For $1<\gamma\leq 3$, by constructing some new control functions ingeniously, we obtain the lower bounds estimates…
In this paper we are interested in the upper bound of the lifespan estimate for the compressible Euler system with time dependent damping and small initial perturbations. We employ some techniques from the blow-up study of nonlinear wave…
We construct the global solution to the Cauchy's problem of the bipolar Euler-Poisson equations with damping in $\mathbb{R}^3$ when $H^3$ norm of the initial data is small. If further, the $\dot{H}^{-s}$ norm ($0\leq s<3/2)$ or…
In this paper, we consider some blow-up problems for the 1D Euler equation with time and space dependent damping. We investigate sufficient conditions on initial data and the rate of spatial or time-like decay of the coefficient of damping…
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…
This paper investigates the global well-posedness and large-time behavior of solutions for a coupled fluid model in $\mathbb{R}^3$ consisting of the isothermal compressible Euler-Poisson system and incompressible Navier-Stokes equations…
In this paper, we study the large-time behavior of solutions to a class of partially dissipative linear hyperbolic systems with applications in velocity-jump processes in several dimensions. Given integers $n,d\ge 1$, let $\mathbf…
In this paper, we prove a time dependent lower bound on density in the optimal order $O(1/(1+t))$ for the general smooth nonisentropic flow of compressible Euler equations.
By a new energy approach involved in the high frequencies and low frequencies decomposition in the Besov spaces, we obtain the optimal decay for the incompressible Oldroyd-B model without damping mechanism in $\mathbb{R}^n$ ($n\ge 2$). More…
This paper is concerned with the asymptotic behavior of the solution to the Euler equations with time-depending damping on quadrant $(x,t)\in \mathbb{R}^+\times\mathbb{R}^+$, \begin{equation}\notag \partial_t v - \partial_x u=0, \qquad…
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…
This paper concerns the long time existence to the smooth solutions of the compressible Euler system with critical time dependent damping in $\R^2$. We establish the sharp lifespan estimate from below, with respect to the small parameter of…
For the physical vacuum free boundary problem of the damped compressible Euler equations in both 2D and 3D, we prove the global existence of smooth solutions and justify their time-asymptotic equivalence to the corresponding Barenblatt…
We investigate the global existence and optimal time decay rate of solution to the one-dimensional (1D) two-phase flow described by compressible Euler equations coupled with compressible Navier-Stokes equations through the relaxation drag…
In this paper, we study the upper bound of the time decay rate of solutions to the Navier-Stokes equations and generalized Navier-Stokes equations with damping term $|u|^{\beta-1}u$ ($\beta>1$) in $\mathbb{R}^3$.
The aim of this paper is to derive higher order energy estimates for solutions to the Cauchy problem for damped wave models with time-dependent propagation speed and dissipation. The model of interest is \begin{equation*}…
Under appropriate assumptions the energy of wave equations with damping and variable coefficients $c(x)u_{tt}-\hbox{div}(b(x)\nabla u)+a(x)u_t =h(x)$ has been shown to decay. Determining the rate of decay for the higher order energies…
We establish the decay of the solutions of the damped wave equations in one dimensional space for the Dirichlet, Neumann, and dynamic boundary conditions where the damping coefficient is a function of space and time. The analysis is based…
In this paper, we consider the one-dimensional isentropic compressible Euler equations with linear damping $\beta(t,x)\rho u$ in a bounded domain, which can be used to describe the process of compressible flows through a porous medium.~And…
We introduce a damping term for the special relativistic Euler equations in $3$-D and show that the equations reduce to the non-relativistic damped Euler equations in the Newtonian limit. We then write the equations as a symmetric…