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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…

Analysis of PDEs · Mathematics 2020-10-20 Fuyi Xu , Meiling Chi , Lishan Liu , Yonghong Wu

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…

Analysis of PDEs · Mathematics 2020-03-03 Xiaoping Zhai , Zhi-Min Chen

The purpose of this work is to investigate the Cauchy problem of global-in-time existence of large strong solutions to the Navier-Stokes equations for compressible viscous and heat conducting fluids. A class of density-dependent viscosity…

Analysis of PDEs · Mathematics 2024-12-04 Yachun Li , Peng Lu , Zhaoyang Shang , Shaojun Yu

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…

Analysis of PDEs · Mathematics 2023-05-18 Zhi Chen , Weixun Feng , Qiao Liu

The purpose of this article is to show that there are many differential viscoelastic models for which the global existence of a regular solution is possible. Although the problem of global existence in the classic Oldroyd model is still…

Analysis of PDEs · Mathematics 2018-07-19 Laurent Chupin

This paper is dedicated to the Cauchy problem of the incompressible Oldroyd-B model with general coupling constant $\om\in (0,1)$. It is shown that this set of equations admits a unique global solution in a certain hybrid Besov spaces for…

Analysis of PDEs · Mathematics 2014-10-29 Ruizhao Zi

In this paper, we consider the 2-dimensional non-viscous Oldroyd-B model. In the case of the ratio equal 1~($\alpha=0$), it is a difficult case since the velocity field $u(t,x)$ is no longer decay. Fortunately, by {observing the exponential…

Analysis of PDEs · Mathematics 2021-10-20 Zhi Chen , Weikui Ye , Zhaoyang Yin

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…

Analysis of PDEs · Mathematics 2024-08-29 Yajuan Zhao , Yongsheng Li , Tao Liang , Xiaoping Zhai

We investigate global strong solutions for the incompressible viscoelastic system of Oldroyd--B type with the initial data close to a stable equilibrium. We obtain the existence and uniqueness of the global solution in a functional setting…

Analysis of PDEs · Mathematics 2011-02-03 Ting Zhang , Daoyuan Fang

In this paper, we study the global regularity and sharp decay rates for the isentropic hypo-viscous compressible Navier-Stokes equations in 1D. Firstly, we prove the global stability for the small initial data near a stable equilibrium.…

Analysis of PDEs · Mathematics 2026-03-17 Chen Liang , Zhaonan Luo , Zhaoyang Yin

In this paper, we study global existence and large time behaviors of strong solutions to the kinetic Cucker--Smale model coupled with the three dimensional incompressible Navier--Stokes equations in the whole space. Using the maximal…

Analysis of PDEs · Mathematics 2021-12-28 Chunyin Jin

We prove the existence of both local and global smooth solutions to the Cauchy problem in the whole space and the periodic problem in the n-dimensional torus for the incompressible viscoelastic system of Oldroyd-B type in the case of near…

Analysis of PDEs · Mathematics 2009-11-13 Zhen Lei , Chun Liu , Yi Zhou

In the first part of this work, we investigate the Cauchy problem for the $d$-dimensional incompressible Oldroyd-B model with dissipation in the stress tensor equation. By developing a weighted Chemin-Lerner framework combined with a…

Analysis of PDEs · Mathematics 2025-04-18 Tao Liang , Yongsheng Li , Xiaoping Zhai

In this paper, we deal with some Oldroyd type models, which describe incompressible viscoelastic fluids. There are 3 parameters in these models: the viscous coefficient of fluid $\nu_{1}$, the viscous coefficient of the elastic part of the…

Analysis of PDEs · Mathematics 2025-07-23 Hantaek Bae , Jaeyong Shin

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…

Analysis of PDEs · Mathematics 2019-10-22 Yong Lu , Milan Pokorný

We show that strong solutions of 2D diffusive Oldroyd-B systems in $\mathbb{R}^2$ decay at an algebraic rate, for a large class of initial data. The main ingredient for the proof is the following fact; an Oldroyd-B system is a macroscopic…

Analysis of PDEs · Mathematics 2018-04-26 Joonhyun La

We explore the existence of global weak solutions to the Hookean dumbbell model, a system of nonlinear partial differential equations that arises from the kinetic theory of dilute polymers, involving the unsteady incompressible…

Analysis of PDEs · Mathematics 2017-07-18 John W. Barrett , Endre Süli

We investigate local and global strong solutions for the incompressible viscoelastic system of Oldroyd--B type. We obtain the existence and uniqueness of a solution in a functional setting invariant by the scaling of the associated…

Analysis of PDEs · Mathematics 2011-02-01 Ting Zhang , Daoyuan Fang

This paper is concerned with a mathematical model which describes 2-D flows of an incompressible viscoelastic fluid of Oldroyd type in a bounded domain. We prove the existence and uniqueness theorem for global (in time) weak solutions and…

Analysis of PDEs · Mathematics 2017-08-15 Mikhail A. Artemov , George G. Berdzenishvili

In this paper, we investigate a three-dimensional fluid-particle coupled model. % in whole space $\mathbb{R}^3$. This model combines the full compressible Navier-Stokes equations with the Vlasov-Fokker-Planck equation via the momentum and…

Analysis of PDEs · Mathematics 2024-08-27 Fucai Li , Jinkai Ni , Man Wu