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The initial value problem for Hookean incompressible viscoelastictic motion in three space dimensions has global strong solutions with small displacements.

Analysis of PDEs · Mathematics 2021-07-01 Boyan Jonov , Paul Kessenich , Thomas C. Sideris

We consider compressible fluid flow on an evolving surface with a piecewise Lipschitz-continuous boundary from an energetic point of view. We employ both an energetic variational approach and the first law of thermodynamics to make a…

Mathematical Physics · Physics 2022-12-20 Hajime Koba

We study the interaction between incompressible viscous fluids and multilayered elastic structures in a 3D/2D/3D framework, where a 3D fluid interacts with a 2D thin elastic layer, coupled to a 3D thick elastic solid. The system is driven…

Analysis of PDEs · Mathematics 2025-01-14 Claudiu Mîndrilă , Arnab Roy

In this paper we study the initial boundary value problem for the system $\Delta v= u_{x_1},\ u_t-\mbox{div}\left(\left((a|\mathbf{q}|+m)I+(b-a)\frac{\mathbf{q}\otimes\mathbf{q}}{|\mathbf{q}|}\right)\nabla u\right)=-\nabla…

Analysis of PDEs · Mathematics 2020-08-26 Xiangsheng Xu

In this paper, we mainly study a hydrodynamic system modeling the flow of nematic liquid crystals. In three dimensions, we first establish local well-posedness of the initial-boundary value problem of the system. Then, we prove the…

Analysis of PDEs · Mathematics 2011-06-03 Wenke Tan , Zhaoyang Yin

We consider a linear second order parabolic system with a third order dispersion term. This type of system arises when considering a nonlinear model equation describing the motion of a vortex filament with axial flow immersed in an…

Analysis of PDEs · Mathematics 2012-01-04 Masashi Aiki , Tatsuo Iguchi

This paper is focused on the generalized Forchheimer flows of slightly compressible fluids in porous media. They are reformulated as a degenerate parabolic equation for the pressure. The initial boundary value problem is studied with…

Analysis of PDEs · Mathematics 2015-10-02 Luan Hoang , Thinh Kieu

We establish the global existence of weak solutions of the isentropic compressible magnetohydrodynamic equations with ripped density in the whole plane provided the bulk viscosity coefficient is properly large. Moreover, we show that such…

Analysis of PDEs · Mathematics 2025-10-31 Shuai Wang , Guochun Wu , Xin Zhong

In this paper, we are concerned with the three-dimensional nonhomogeneous B\'enard system with density-dependent viscosity in bounded domain. The global well-posedness of strong solution is established, provided that the initial total mass…

Analysis of PDEs · Mathematics 2023-10-13 Huanyuan Li , Jieqiong Liu

In this paper, we investigate a system coupled by nonhomogeneous incompressible Navier-Stokes equations and Allen-Cahn equations describing a diffuse interface for two-phase flow of viscous fluids with different densities in a bounded…

Analysis of PDEs · Mathematics 2025-03-06 Yinghua Li , Wenlin Ye

In this work, we study the initial boundary value problem for a non-strictly hyperbolic $2\times2$ system of equations in the quarter plane $x>0,t>0$ which is derived from Eulerian droplet model for air particle flow for velocity and volume…

Analysis of PDEs · Mathematics 2025-07-03 Kayyunnapara Divya Joseph

We concern with the global existence and large time behavior of compressible fluids (including the inviscid gases, viscid gases, and Boltzmann gases) in an infinitely expanding ball. Such a problem is one of the interesting models in…

Analysis of PDEs · Mathematics 2018-09-26 Gang Xu , Huicheng Yin

In this paper, we consider the three-dimensional isentropic Navier-Stokes equations for compressible fluids with viscosities depending on density in a power law and allowing initial vacuum. We introduce the notion of regular solutions and…

Analysis of PDEs · Mathematics 2015-04-14 Yachun Li , Ronghua Pan , Shengguo Zhu

The study of global-in-time dynamics of vacuum is crucial for understanding viscous flows. In particular, physical vacuum, characterized by a moving boundary with nontrivial finite normal acceleration, naturally arises in the motion of…

Analysis of PDEs · Mathematics 2026-02-03 Gui-Qiang G. Chen , Jiawen Zhang , Shengguo Zhu

For the natural initial conditions $L^1$ in the density field (more generally a positive bounded Radon measure) and $L^\infty$ in the velocity field we obtain global approximate solutions to the Cauchy problem for the 3-D systems of…

Analysis of PDEs · Mathematics 2014-06-03 Mathilde Colombeau

In this paper, we establish some local and global solutions for the two phase incompressible inhomogeneous flows with moving interfaces in $L_p-L_q$ maximal regularity class. Compared with previous results obtained by V.A.Solonnikov and by…

Analysis of PDEs · Mathematics 2018-11-07 Hirokazu Saito , Yoshihiro Shibata , Xin Zhang

In this paper, we establish a priori estimates for the three-dimensional compressible Euler equations with moving physical vacuum boundary, the $\gamma$-gas law equation of state for $\gamma=2$ and the general initial density $\ri \in H^5$.…

Analysis of PDEs · Mathematics 2013-06-21 Chengchun Hao

In this paper, we study the compressible viscoelastic equations in an exterior domain. We prove the $L_2$ estimates for the solution to the linearized problem and show the decay estimates for the solution to the nonlinear problem. In…

Analysis of PDEs · Mathematics 2025-06-10 Jieling Deng , Yong Wang , Jianquan Yang

The one-dimensional fractional derivative Maxwell model (e.g. Palade et al. Rheol. Acta 35, 265, 1996), of importance in modeling the linear viscoelastic response in the glass transition region, has been generalized in Palade et al. Int. J.…

Analysis of PDEs · Mathematics 2011-03-18 Arnaud Heibig , Liviu Iulian Palade

Time fractional advection-dispersion equations arise as generalizations of classical integer order advection-dispersion equations and are increasingly used to model fluid flow problems through porous media. In this paper we develop an…

Numerical Analysis · Mathematics 2019-05-16 Carlos E. Mejía , Alejandro Piedrahita