Related papers: Optimal time-decay estimates for an Oldroyd-B mode…
In this paper, we consider the Cauchy problem for an inviscid compressible Oldroyd-B model in three dimensions. The global well posedness of strong solutions and the associated time-decay estimates in Sobolev spaces are established near an…
A two-dimensional inviscid and diffusive Oldroyd-B model was investigated by [T. M. Elgindi, F. Rousset, Commun. Pure Appl. Math. 68 (2015), 2005--2021] where the global existence and uniqueness of the strong solution were established for…
In this paper, we study the optimal time decay rates for the higher order spatial derivatives of solutions to a diffusive Oldroyd-B model. As pointed out in the Section 1.2 of Huang-Wang-Wen-Zi (J. Differential Equations 306: 456-491,…
In this paper, we are concerned with optimal decay rate for the 2-D generalized Oldroyd-B model with only stress tensor diffusion $(-\Delta)^{\beta}\tau$. In the case $\beta=1$, we first establish optimal decay rate in $H^1$ framework and…
This paper is devoted to studying the Cauchy problem for the three-dimensional isentropic compressible Navier-Stokes equations with density-dependent viscosities given by $\mu=\rho^\alpha,\lambda=\rho^\alpha(\alpha>0)$. We establish the…
This paper is devoted to the uniform vanishing damping limit of the 2D inviscid Oldroyd-B model with fractional stress tensor diffusion. Firstly, we find that fractional stress tensor diffusion helps to reduce the global regularity of the…
We are concerned with the time decay rates of strong solutions to a non-conservative compressible viscous two-phase fluid model in the whole space R3. Compared to the previous related works, the main novelty of this paper lies in the fact…
The Cauchy problem of the compressible Oldroyd-B model without damping mechanism in R^n$ with $n\ge2$ is considered. The lack of dissipation in density and stress tensor in the model is compensated by exploiting an intrinsic structure and…
We consider the global existence and large-time asymptotic behavior of strong solutions to the Cauchy problem of the three-dimensional nonhomogeneous incompressible Navier-Stokes equations with density-dependent viscosity and vacuum. We…
In this paper, we investigate the global well-posedness and optimal time-decay of classical solutions for the 3-D full compressible Navier-Stokes system, which is given by the motion of the compressible viscous and heat-conductive gases.…
This paper investigates the global existence and the decay rate in time of a solution to the Cauchy problem for an incompressible Oldroyd model with a deformation tensor damping term. There are three major results. The first is the global…
In this paper, the Cauchy problem for the three-dimensional (3-D) isentropic compressible Navier-Stokes equations with degenerate viscosities is considered. By introducing some new variables and making use of the "quasi-symmetric…
We establish the time decay rates of the solution to the Cauchy problem for the compressible Navier-Stokes-Poisson system via a refined pure energy method. In particular, the optimal decay rates of the higher-order spatial derivatives of…
In this paper, the Cauchy problem for the three-dimensional (3-D) isentropic compressible Navier-Stokes equations is considered. When viscosity coefficients are given as a constant multiple of the density's power ($\rho^\delta$ with…
We consider the Cauchy problem on nonlinear scalar conservation laws with a diffusion-type source term related to an index $s\in \R$ over the whole space $\R^n$ for any spatial dimension $n\geq 1$. Here, the diffusion-type source term…
The present paper deals with the Cauchy problem of a multi-dimensional non-conservative viscous compressible two-fluid system. We first study the well-posedness of the model in spaces with critical regularity indices with respect to the…
In this paper, we are concerned with long time behavior of the strong solutions to the 2-D compressible Oldroyd-B and Hall-MHD model. By virtue of the improved Fourier splitting method and the time weighted energy estimate, we obtain the…
We prove sharp estimates for the decay in time of solutions to a rather general class of non-local in time subdiffusion equations on a bounded domain subject to a homogeneous Dirichlet boundary condition. Important special cases are the…
We are concerned with the study of the Cauchy problem to the 3D compressible Hall-magnetohydrodynamic system. We first establish the unique global solvability of strong solutions to the system when the initial data are close to a stable…
In this paper, we consider the Cauchy problem for a compressible Oldroyd-B model in three dimensions. Under some smallness assumptions on the initial data, we obtain the global wellposedness of strong solution with uniform regularity.…