相关论文: Global existence and optimal decay rate of weak so…

In this paper, we are concerned with global strong solutions and large time behavior for some inviscid Oldroyd-B models. We first establish the energy estimate and B-K-M criterion for the 2-D co-rotation inviscid Oldroyd-B model. Then, we…

In this paper, we consider global strong solutions and uniform-in-time vanishing damping limit for the inviscid Oldroyd-B model in R^d, where d=2 and 3. The well-recognized problem of the global existence of smooth solutions for the 2D…

This paper studies the global well-posedness and optimal decay estimates to the Oldroyd-B model in $\mathbb R^d$ ($d\geq2$). By utilizing the special structure of this system, we give a simplified proof to the global existence of solutions…

We start with the compressible Oldroyd--B model derived in \cite{Barrett-Lu-Suli} ({\em J. W. Barrett, Y. Lu, E. S\"uli. Existence of large-data finite-energy global weak solutions to a compressible Oldroyd--B model. Comm. Math. Sci. 15…

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, we mainly study global existence and optimal $L^2$ decay rate of weak solutions to the co-rotation Hooke dumbbell model. This micro-macro model is a coupling of the Navier-Stokes equation with a nonlinear Fokker-Planck…

We study the $d$-dimensional ($d\geq2$) incompressible Oldroyd-B model with only stress tensor diffusion and without velocity dissipation as well as the damping mechanism on the stress tensor. Firstly, based upon some new observations on…

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 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…

A compressible Oldroyd--B type model with stress diffusion is derived from a compressible Navier--Stokes--Fokker--Planck system arising in the kinetic theory of dilute polymeric fluids, where polymer chains immersed in a barotropic,…

We consider the Cauchy problem ($\mathbb{R}^d, d=2,3$) and the initial boundary values problem ($\mathbb{T}^d, d=2,3$)associated to the compressible Oldroyd-B model which is first derived by Barrett, Lu and S\"{u}li [Existence of large-data…

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…

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…

In this paper, we prove the global existence of small smooth solutions to the three-dimensional incompressible Oldroyd-B model without damping on the stress tensor. The main difficulty is the lack of full dissipation in stress tensor. To…

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 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…

In this paper, we consider the global regularity and the optimal time decay rate for the 2D isentropic hypo-viscous compressible Navier-Stokes equations. Firstly, we prove that there exists a global strong solution with the small initial…

In this paper, we are concerned with global existence and optimal decay rates of solutions for the three-dimensional compressible Hall-MHD equations. First, we prove the global existence of strong solutions by the standard energy method…

The purpose of this work is to study the global wellposedness and large time behavior results of strong solutions for the compressible Oldroyd-B model derived by Barrett, Lu, S\"uli (Commun. Math. Sci., 15, 1265--1323, 2017). Exploiting the…

We obtain the global small solutions to the generalized Oldroyd-B model without damping on the stress tensor in $\mathbb{R}^n$. Our result give positive answers partially to the question proposed by Elgindi and Liu (Remark 2 in Elgindi and…