English
Related papers

Related papers: Global Strong Solution for Large Data to the Hyper…

200 papers

We consider a three-dimensional domain occupied by a homogeneous, incompressible, non-Newtonian, heat-conducting fluid with prescribed nonuniform temperature on the boundary and no-slip boundary conditions for the velocity. No external body…

Analysis of PDEs · Mathematics 2026-01-26 Anna Abbatiello , Miroslav Bulíček , Petr Kaplický

In [1], the Authors rigorously establish the relaxation limit from the Quantum Navier Stokes Poisson (QNSP) system to the Quantum Drift Diffusion (QDD) equation, while providing only a brief outline of the global existence theory for weak…

Analysis of PDEs · Mathematics 2025-12-10 Giada Cianfarani Carnevale

In this paper, we present a refined framework for the global-in-time well-posedness theory for the pressureless Euler--Navier--Stokes system and the optimal temporal decay rates of certain norms of solutions. Here the coupling of two…

Analysis of PDEs · Mathematics 2023-07-10 Young-Pil Choi , Jinwook Jung , Junha Kim

We consider the 3D isentropic compressible Navier-Stokes equations with degenerate viscousities and vacuum. The degenerate viscosities $\mu(\rho)$ and $\lambda(\rho)$ are proportional to some power of density, while the powers of density in…

Analysis of PDEs · Mathematics 2024-09-30 Yachun Li , Shaojun Yu

This paper concerns the existence of global weak solutions to the barotropic compressible Navier-Stokes equations with degenerate viscosity coefficients. We construct suitable approximate system which has smooth solutions satisfying the…

Analysis of PDEs · Mathematics 2015-11-12 Jing Li , Zhouping Xin

In this paper, we simplify and extend the results of \cite{GZ} to include the case in which $\Om =\R^3$. Let ${[L^2({\mathbb{R}}^3)]^3}$ be the Hilbert space of square integrable functions on ${\mathbb {R}}^3 $ and let ${\mathbb…

Mathematical Physics · Physics 2010-09-17 Tepper L. Gill , Woodford W. Zachary

We consider a non-Newtonian incompressible heat conducting fluid with prescribed nonuniform temperature on the boundary and with the no-slip boundary conditions for the velocity. We assume no external body forces. For the power-law like…

Analysis of PDEs · Mathematics 2022-10-21 Anna Abbatiello , Miroslav Bulíček , Petr Kaplický

In 1901, Korteweg formulated a constitutive equation for the Cauchy stress tensor to provide a continuum mechanical model for capillarity within fluids. Dunn and Serrin [Arch. Ration. Mech. Anal. 88(2):95-133,1985] in 1985 further modified…

Analysis of PDEs · Mathematics 2026-03-13 Yongteng Gu , Xiangdi Huang , Weili Meng , Huitao Zhou

In this paper, we consider the global well-posedness problem of the isentropic compressible Navier-Stokes equations in the whole space $\R^N$ with $N\ge2$. In order to better reflect the characteristics of the dispersion equation, we make…

Analysis of PDEs · Mathematics 2016-08-24 Daoyuan Fang , Ting Zhang , Ruizhao Zi

This work is devoted to prove the existence of global strong solution in dimension $N\geq 2$ for a isothermal model of capillary fluids derived by J.E Dunn and J.Serrin (1985) (see \cite{fDS}), which can be used as a phase transition model.…

Analysis of PDEs · Mathematics 2016-06-14 Boris Haspot

In this paper, we are concerned with the system of the non-isentropic compressible Navier-Stokes equations coupled with the Maxwell equations through the Lorentz force in three space dimensions. The global existence of solutions near…

Analysis of PDEs · Mathematics 2015-12-29 Qingqing Liu , Yifan Su

The global-in-time existence of weak solutions to the barotropic compressible quantum Navier-Stokes equations with damping is proved for large data in three dimensional space. The model consists of the compressible Navier-Stokes equations…

Analysis of PDEs · Mathematics 2015-08-26 Alexis F. Vasseur , Cheng Yu

The object of the present paper is to show the existence and the uniqueness of a reproductive strong solution of the Navier-Stokes equations, i.e. the solution $\boldsymbol{u} $ belongs to $\text{}\mathbf{L}% ^{\infty}(0,T;V) \cap…

Analysis of PDEs · Mathematics 2007-05-23 Chérif Amrouche , Macaire Batchi , Jean Batina

We are concerned with the large-time behavior of solutions to the initial and initial boundary value problems with large initial data for the compressible Navier-Stokes system with degenerate heat-conductivity describing the one-dimensional…

Analysis of PDEs · Mathematics 2024-07-19 Kexin Li , Xiaojing Xu

In this paper, we study a free boundary problem for compressible spherically symmetric Navier-Stokes equations with a gravitational force and degenerate viscosity coefficients. Under certain assumptions that imposed on the initial data, we…

Analysis of PDEs · Mathematics 2007-05-23 Mingjun Wei , Ting Zhang , Daoyuan Fang

The current paper is devoted to the investigation of the global-in-time stability of large solutions for the full Navier-Stokes-Fourier system in the whole space. Suppose that the density and the temperature are bounded from above uniformly…

Analysis of PDEs · Mathematics 2020-01-06 Lingbing He , Jingchi Huang , Chao Wang

We are concerned with the isentropic compressible Navier-Stokes system in the two-dimensional torus, with rough data and vacuum : the initial velocity is in the Sobolev space H^1 and the initial density is only bounded and nonnegative.…

Analysis of PDEs · Mathematics 2023-11-03 Raphaël Danchin , Shan Wang

We prove the global existence and uniqueness of the classical (weak) solution for the 2D or 3D compressible Navier-Stokes equations with a density-dependent viscosity coefficient ($\lambda=\lambda(\rho)$). Initial data and solutions are…

Analysis of PDEs · Mathematics 2009-04-13 Ting Zhang

In this paper we study a coupled system modeling the movement of a deformable solid immersed in a fluid. For the solid we consider a given deformation that has to obey several physical constraints. The motion of the fluid is modeled by the…

Analysis of PDEs · Mathematics 2014-07-08 Sébastien Court

This paper is dedicated to the global existence and optimal decay estimates of strong solutions to the compressible viscoelastic flows in the whole space $\mathbb{R}^n$ with any $n\geq2$. We aim at extending those works by Qian \& Zhang and…

Analysis of PDEs · Mathematics 2022-08-08 Xinghong Pan , Jiang Xu