GEVREY CLASS REGULARITY FOR THE GLOBAL ATTRACTOR OF A TWO-DIMENSIONAL NON-NEWTONIAN FLUID

This article investigates Gevrey class regularity for the global attractor of an incompressible non-Newtonian fluid in a two-dimensional domain with a periodic boundary condition.This Gevrey class regularity reveals that the solutions lying in the global attractor are analytic in time with values in a Gevrey class of analytic functions in space.

Gevrey Class Regularity and Exponential Decay Property for Navier-Stokes-α Equations

The Navier-Stokes-α equations subject to the periodic boundary conditions are considered. Analyticity in time for a class of solutions taking values in a Gevrey class of functions is proven. Exponential decay of the spatial Fourier spectrum for the analytic solutions and the lower bounds on the rate defined by the exponential decay are also obtained.

GEVREY-HYPOELLIPTICITY FOR A CLASS OF TOTALLY CHARACTERISTIC OPERATORS

This paper deals with the Gevreg-hypoellipticity for a class of totally characteristic operators with the elliptic condition and the discrete boundary spectrum condition respectively.

NONLINEAR HYPERBOLIC CAUCHY PROBLEMS IN GEVREY CLASSES

The authors prove well posedness in Gevrey classes of Cauchy problem for nonlinear hyper- bolic equations of constant multiplicity with Holder dependence on the time variable.

Zero Viscosity-Diffusivity Limit for the Incompressible Boussinesq Equations in Gevrey Class

In this paper,we study the zero viscosity-diffusivity limit for the incompressible Boussinesq equations in a periodic domain in the framework of Gevrey class.We first prove that there exists an interval of time,independent of the viscosity coefficient and the diffusivity coefficient,for the solutions to the viscous incompressible Boussinesq equations.Then,based on these uniform estimates,we show that the solutions of the viscous incompressible Boussinesq equations converge to that of the ideal incompressible Boussinesq equations as the viscosity and diffusivity coefficients go to zero.Moreover,the convergence rate is alsogiven.

Gevrey Class Regularity of a Semigroup Associated with a Nonlinear Korteweg-de Vries Equation

In this paper, the authors consider the Gevrey class regularity of a semigroup associated with a nonlinear Korteweg-de Vries （KdV for short） equation. By estimating the resolvent of the corresponding linear operator, the authors conclude that the semigroup 3 generated by the linear operator is not analytic but of Gevrey class δ ε （5, ） for t 〉 0,

GEVREY CLASS REGULARITY AND APPROXIMATE INERTIAL MANIFOLDS FOR THE NEWTON-BOUSSINESQ EQUATIONS

The authors show the Gevrey class regularity of the solutions for the two-dimensional Newton-Boussinesq Equations. Based on this fact, an approximate inertial manifold for the system is constructed, which attracts all solutions to an exponentially thin neighborhood of it in a finite time.

GEVREY REGULARITY WITH WEIGHT FOR INCOMPRESSIBLE EULER EQUATION IN THE HALF PLANE

In this work we prove the weighted Gevrey regularity of solutions to the incompressible Euler equation with initial data decaying polynomially at infinity. This is motivated by the well-posedness problem of vertical boundary layer equation for fast rotating fluid. The method presented here is based on the basic weighted L;-estimate, and the main difficulty arises from the estimate on the pressure term due to the appearance of weight function.

Long-Time Behaviour of the Solutions for the Multidimensional Kolmogorov-Spieqel-Sivashinsky Equation

In this paper, we study the existence and long-time behaviour of the solutions for the multidimensional Kolmogorov-Spiegel-Sivashinsky equation. We first show the existence of the global solution for this equation, and then prove the existence of the global attractor and establish the esti- mates of the upper bounds of Hausdorff and fractal dimensions for the attractor. We also obtain the Gevrey class regularity for the solutions and construct an approximate inertial manifold for the system.