Related papers: Finite Dimensionality of the Global Attractor for …
We establish the global existence and uniqueness of strong solutions to the initial boundary value problem for incompressible MHD equations in a bounded smooth domain of three spatial dimensions with initial density being allowed to have…
In this work the existence and properties of a global attractor for the solution semiflow of the Oregonator system are proved. The Oregonator system is the mathematical model of the famous Belousov-Zhabotinskii reaction. A rescaling and…
In this paper, we consider the initial-boundary value problem of the 3D primitive equations for planetary oceanic and atmospheric dynamics with only horizontal eddy viscosity in the horizontal momentum equations and only horizontal…
We consider a nonlocal nonlinear model with fractional diffusion motivated by studies of electroconvection phenomena in incompressible viscous fluids. We address the global well-posedness, global regularity and long time dynamics of the…
The existence and uniqueness of the global strong solution with small initial data to the three-dimensional viscoelastic fluids is established.
We give the explicit estimates of order $\gamma^{-d}$ (with logarithmic correction in the 1D case) for the fractal dimension of the attractor of the damped hyperbolic equation (or system) in a bounded domain $\Omega\subset \mathbb R^d$,…
This paper is devoted to initial-boundary value problem of an extensible beam equation with degenerate nonlocal energy damping in $\Omega\subset\mathbb{R}^n$: $u_{tt}-\kappa\Delta u+\Delta^2u-\gamma(\Vert \Delta u\Vert^2+\Vert…
We consider three dimensional incompressible Navier-Stokes equation $(NS)$ with different viscous coefficient in the vertical and horizontal variables. In particular, when one of these viscous coefficients is large enough compared to the…
In this paper, we consider the Dirichlet problem of three-dimensional inhomogeneous incompressible micropolar equations with density-dependent viscosity. Under the assumption that the coefficients are power functions of the density, we…
We consider Navier-Stokes equations for compressible viscous fluids in one dimension. We prove the existence of global strong solution with large initial data for the shallow water system. The key ingredient of the proof relies to a new…
We investigate the long-time behavior of a nonlocal Cahn-Hilliard equation in a bounded domain $\Omega\subset\mathbb{R}^d$ $(d\in\{2,3\})$, subject to a kinetic rate-dependent nonlocal dynamic boundary condition. The kinetic rate $1/L$,…
We investigate the initial-value problem for the incompressible tangential Navier-Stokes equation with variable viscosity on a given two-dimensional surface without boundary. Existence of global weak and strong solutions under inhomogeneous…
Partial Differential Equations (PDEs) play a crucial role as tools for modeling and comprehending intricate natural processes, notably within the domain of biology. This research explores the domain of microbial activity within the complex…
We regularized the 3D Navier-Stokes equations by adding a fourth-order viscosity term. We study the upper semicontinuity, of the global attractors of the Leray-Hopf weak solutions of the regularized 3D Navier-Stokes equations, as the…
We consider a two-dimensional MHD model describing the evolution of viscous, compressible and electrically conducting fluids under the action of vertical magnetic field without resistivity. Existence of global weak solutions is established…
In view of the possibility that the 3D Navier-Stokes equations (NSE) might not always have regular solutions, we introduce an abstract framework for studying the asymptotic behavior of multi-valued dissipative evolutionary systems with…
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…
We derive the general analytical solution of the viscous hydrodynamic equations for an ultrarelativistic gas of hard spheres undergoing Bjorken expansion, taking into account effects from particle number conservation, and use it to…
In this paper, we study the global wellposedness of a radiation hydrodynamics model with viscosity and thermal conductivity. It is now well-understood that, unlike the compressible Euler equations whose smooth solutions must blow up in…
This paper is concerned with the global solvability for the Navier-Stokes equations describing viscous free surface flows of infinite depth in three and higher dimensions. We first prove time weighted estimates of solutions to a linearized…