相关论文: The global attractor for the 3-D viscous primitive…

In this paper we study the structure of the global attractor for a reaction- di{\S}usion equation in which uniqueness of the Cauchy problem is not guarantied. We prove that the global attractor can be characterized using either the unstable…

We establish global well-posedness of strong solutions for the nonhomogeneous magnetohydrodynamic equations with density-dependent viscosity and initial density allowing vanish in two-dimensional (2D) bounded domains. Applying delicate…

We consider a Nicholson's equation with multiple pairs of time-varying delays and nonlinear terms given by mixed monotone functions. Sufficient conditions for the permanence, local stability and global attractivity of its positive…

This paper considers the Cauchy problem of equations for the viscous compressible and heat-conductive fluids in the two-dimensional(2D) space. We establish the local existence theory of unique strong solution under some initial layer…

We consider the nonlinear integrodifferential Benjamin-Bona-Mahony equation $$ u_t - u_{txx} + u_x - \int_0^\infty g(s) u_{xx}(t-s) {\rm d} s + u u_x = f $$ where the dissipation is entirely contributed by the memory term. Under a suitable…

We study the existence and uniqueness of a bounded weak solution for a triply nonlinear thermistor problem in Sobolev spaces. Furthermore, we prove the existence of an absorbing set and, consequently, the universal attractor.

The authors study the Cauchy problem of the magnetohydrodynamic equations for viscous compressible barotropic flows in two or three spatial dimensions with vacuum as far field density. For two spatial dimensions, we establish the global…

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…

In the article, we aim to investigate the well-posedness of solution and the regularity of the global attractor for the couple stress fluid in saturated porous media with the local thermal non-equilibrium effect. To be more specific, we…

In this paper, we prove the existence of global weak solutions to the compressible two-fluid Navier-Stokes equations in three dimensional space. The pressure depends on two different variables from the continuity equations. We develop an…

An abstract framework for studying the asymptotic behavior of a dissipative evolutionary system $\mathcal{E}$ with respect to weak and strong topologies was introduced in [8] primarily to study the long-time behavior of the 3D Navier-Stokes…

Well-posedness and global attractor are established for 2D damped driven nonlinear Schr\"odinger equation with almost periodic pumping in a bounded region. The key role is played by a novel application of the energy equation.

This article establishes estimates on the dimension of the global attractor of the two-dimensional rotating Navier-Stokes equation for viscous, incompressible fluids on the $\beta$-plane. Previous results in this setting by M.A.H.…

We establish the global well-posedness of classical solutions to the vacuum free boundary problem of the 1-D viscous Saint-Venant system with large data. Since the depth $\rho$ of the fluid vanishes on the moving boundary, the momentum…

We present a computer assisted method for proving the existence of globally attracting fixed points of dissipative PDEs. An application to the viscous Burgers equation with periodic boundary conditions and a forcing function constant in…

In this paper we are concerned with the global well-posedness for the compressible MHD equations with large data. We show that if the shear viscosity $\mu$ is a positive constant and the bulk viscosity $\lambda$ is the power function of the…

We establish a smoothing result for the generalized KdV (gKdV) on the torus with polynomial non-linearity, damping, and forcing that matches the smoothing level for the gKdV at $H^1$. As a consequence, we establish the existence of a global…

We study the set of solutions of the complex Ginzburg-Landau equation in $\real^d, d<3$. We consider the global attracting set (i.e., the forward map of the set of bounded initial data), and restrict it to a cube $Q_L$ of side $L$. We cover…

The full heat-conducting compressible primitive equations are considered, extending the compressible primitive-equation framework by coupling the temperature through the ideal gas law and the thermal energy balance in the presence of…

The long-term behaviour of solutions to a model for acoustic-structure interactions is addressed; the system is comprised of coupled semilinear wave (3D) and plate equations with nonlinear damping and critical sources. The questions of…